alpha = 0.0033333333333333335
N=10, K=2
MLE: bias <-0.04444322409942374>, mab <0.11604042719855058, mse <0.026367094740885465>
Horvitz-Thompson: bias <-0.012289721092048681>, mab <0.11241437574812305, mse <0.02522997724384085>
Chao-Shen: bias <0.002158913777603281>, mab <0.11570822007760741, mse <0.027213811447574635>
Miller-Madow: bias <-0.0029932240994236573>, mab <0.1266728186163318, mse <0.028077725193687477>
Jackknife: bias <0.011514175906576125>, mab <0.12802795603382824, mse <0.02845696800044592>
NSB: bias <0.14770071160140358>, mab <0.19734516057978504, mse <0.051849647188431124>
MLE vs. Horvitz-Thompson: greater mab <0.0151> (False), greater mse <0.0161> (False)
MLE vs. Chao-Shen: greater mab <0.448> (False), greater mse <0.8438> (False)
MLE vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
MLE vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9998> (True)
MLE vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9994> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9079> (False)
Chao-Shen vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9945> (False)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.9726> (False), greater mse <0.9629> (False)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=100, K=2
MLE: bias <-0.002434475992036627>, mab <0.0329941837764777, mse <0.0021382556265252986>
Horvitz-Thompson: bias <-0.0014775378285486838>, mab <0.032799544804777925, mse <0.0021053146149388265>
Chao-Shen: bias <-0.0012661993716636642>, mab <0.03289428899323013, mse <0.002108124494673359>
Miller-Madow: bias <0.0024705240079633743>, mab <0.03325888047091587, mse <0.0021496783446603575>
Jackknife: bias <0.0027113137265169624>, mab <0.03319615131945544, mse <0.002143999270657144>
NSB: bias <0.013235317427186206>, mab <0.03577339479546043, mse <0.0023062659627920896>
MLE vs. Horvitz-Thompson: greater mab <0.0394> (False), greater mse <0.0017> (True)
MLE vs. Chao-Shen: greater mab <0.2391> (False), greater mse <0.0121> (False)
MLE vs. Miller-Madow: greater mab <0.9584> (False), greater mse <0.7822> (False)
MLE vs. Jackknife: greater mab <0.8966> (False), greater mse <0.6463> (False)
MLE vs. NSB: greater mab <0.9999> (True), greater mse <0.9997> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9849> (False), greater mse <0.8016> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9968> (True), greater mse <0.9983> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.9913> (False), greater mse <0.9959> (False)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9746> (False), greater mse <0.9937> (False)
Chao-Shen vs. Jackknife: greater mab <0.9489> (False), greater mse <0.9847> (False)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0043> (False), greater mse <0.0011> (True)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=1000, K=2
MLE: bias <-0.001288175550651364>, mab <0.010504626094094327, mse <0.0002111288774958691>
Horvitz-Thompson: bias <-0.0012800338452331943>, mab <0.010498195549599102, mse <0.00021109907535180598>
Chao-Shen: bias <-0.0012790393276921168>, mab <0.010498850670444345, mse <0.00021109972688097812>
Miller-Madow: bias <-0.0007881755506514005>, mab <0.010474643418325283, mse <0.00021009070194521746>
Jackknife: bias <-0.0007856309276595467>, mab <0.010473697243679816, mse <0.0002100766041600453>
NSB: bias <3.975505380896835e-05>, mab <0.010469117226214292, mse <0.00020923266425605221>
MLE vs. Horvitz-Thompson: greater mab <0.0966> (False), greater mse <0.1291> (False)
MLE vs. Chao-Shen: greater mab <0.0949> (False), greater mse <0.1278> (False)
MLE vs. Miller-Madow: greater mab <0.0309> (False), greater mse <0.0125> (False)
MLE vs. Jackknife: greater mab <0.0251> (False), greater mse <0.0115> (False)
MLE vs. NSB: greater mab <0.1988> (False), greater mse <0.0637> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9999> (True), greater mse <0.5006> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0747> (False), greater mse <0.015> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.0659> (False), greater mse <0.0143> (False)
Horvitz-Thompson vs. NSB: greater mab <0.2393> (False), greater mse <0.0671> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.0684> (False), greater mse <0.0149> (False)
Chao-Shen vs. Jackknife: greater mab <0.0554> (False), greater mse <0.0132> (False)
Chao-Shen vs. NSB: greater mab <0.2363> (False), greater mse <0.0701> (False)
Miller-Madow vs. Jackknife: greater mab <0.0046> (False), greater mse <0.0013> (True)
Miller-Madow vs. NSB: greater mab <0.4131> (False), greater mse <0.129> (False)
Jackknife vs. NSB: greater mab <0.4296> (False), greater mse <0.138> (False)


N=10000, K=2
MLE: bias <-8.595578850650958e-05>, mab <0.003296953668855467, mse <2.1094453724005197e-05>
Horvitz-Thompson: bias <-8.595578093123617e-05>, mab <0.0032969536612801943, mse <2.109445370135357e-05>
Chao-Shen: bias <-8.595578093123617e-05>, mab <0.0032969536612801943, mse <2.109445370135357e-05>
Miller-Madow: bias <-3.5955788506514955e-05>, mab <0.003298585692266688, mse <2.108835814515456e-05>
Jackknife: bias <-3.593529267958054e-05>, mab <0.00329858505806458, mse <2.1088352402136852e-05>
NSB: bias <4.6336513501354954e-05>, mab <0.003303200155022279, mse <2.108863893961411e-05>
MLE vs. Horvitz-Thompson: greater mab <0.0329> (False), greater mse <0.1208> (False)
MLE vs. Chao-Shen: greater mab <0.0353> (False), greater mse <0.1271> (False)
MLE vs. Miller-Madow: greater mab <0.8446> (False), greater mse <0.3317> (False)
MLE vs. Jackknife: greater mab <0.8514> (False), greater mse <0.3407> (False)
MLE vs. NSB: greater mab <0.9316> (False), greater mse <0.4414> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.8509> (False), greater mse <0.3399> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.8541> (False), greater mse <0.3344> (False)
Horvitz-Thompson vs. NSB: greater mab <0.9313> (False), greater mse <0.4439> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.8492> (False), greater mse <0.3343> (False)
Chao-Shen vs. Jackknife: greater mab <0.8497> (False), greater mse <0.3432> (False)
Chao-Shen vs. NSB: greater mab <0.9348> (False), greater mse <0.4496> (False)
Miller-Madow vs. Jackknife: greater mab <0.3857> (False), greater mse <0.3145> (False)
Miller-Madow vs. NSB: greater mab <0.964> (False), greater mse <0.5116> (False)
Jackknife vs. NSB: greater mab <0.9618> (False), greater mse <0.5041> (False)


alpha = 0.0033333333333333335
N=10, K=5
MLE: bias <-0.201762960798748>, mab <0.23894411956462522, mse <0.09346309612978748>
Horvitz-Thompson: bias <-0.032371272953240555>, mab <0.2288605409861487, mse <0.08524760407415244>
Chao-Shen: bias <-0.015151966014548277>, mab <0.22653729156995786, mse <0.0841830922039591>
Miller-Madow: bias <-0.07426296079874815>, mab <0.2095152320160739, mse <0.07396586500614288>
Jackknife: bias <-0.005785758722055018>, mab <0.22426992005756838, mse <0.08071883244987177>
NSB: bias <0.19027579683227283>, mab <0.3040012634779115, mse <0.13797571769001007>
MLE vs. Horvitz-Thompson: greater mab <0.0265> (False), greater mse <0.0023> (True)
MLE vs. Chao-Shen: greater mab <0.0154> (False), greater mse <0.0032> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0042> (False), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0109> (False), greater mse <0.0605> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0006> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Jackknife: greater mab <0.1209> (False), greater mse <0.0018> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=100, K=5
MLE: bias <-0.022120055549131826>, mab <0.05533820985773583, mse <0.005049935806390004>
Horvitz-Thompson: bias <-0.013040348165926734>, mab <0.05269941190286257, mse <0.004558663298664998>
Chao-Shen: bias <-0.013161202438341096>, mab <0.052689790420863435, mse <0.004551894070367785>
Miller-Madow: bias <-0.0030900555491318333>, mab <0.05261122058293761, mse <0.004625556590790262>
Jackknife: bias <-0.0012539302961726965>, mab <0.052338543386898174, mse <0.0045746717153927>
NSB: bias <0.009845634551868956>, mab <0.05302395345681342, mse <0.004653491007265658>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0075> (False), greater mse <0.0016> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.4049> (False), greater mse <0.0707> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.4263> (False), greater mse <0.8604> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.2202> (False), greater mse <0.6047> (False)
Horvitz-Thompson vs. NSB: greater mab <0.6746> (False), greater mse <0.8259> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.4415> (False), greater mse <0.8777> (False)
Chao-Shen vs. Jackknife: greater mab <0.2294> (False), greater mse <0.645> (False)
Chao-Shen vs. NSB: greater mab <0.6757> (False), greater mse <0.8429> (False)
Miller-Madow vs. Jackknife: greater mab <0.0006> (True), greater mse <0.0002> (True)
Miller-Madow vs. NSB: greater mab <0.844> (False), greater mse <0.6765> (False)
Jackknife vs. NSB: greater mab <0.977> (False), greater mse <0.9404> (False)


N=1000, K=5
MLE: bias <-0.0016258288778063636>, mab <0.01607620399634607, mse <0.0004403987678919504>
Horvitz-Thompson: bias <-0.0014543461079174148>, mab <0.016032820791101247, mse <0.00043920266822054235>
Chao-Shen: bias <-0.0014570211875505243>, mab <0.016034171610420003, mse <0.00043925762161930694>
Miller-Madow: bias <0.00036217112219363834>, mab <0.01598031481848099, mse <0.00043808365226783867>
Jackknife: bias <0.0003908061780583699>, mab <0.015975567094286717, mse <0.0004379582360079547>
NSB: bias <0.001020028874111617>, mab <0.015986659355040386, mse <0.0004384448201878431>
MLE vs. Horvitz-Thompson: greater mab <0.0222> (False), greater mse <0.104> (False)
MLE vs. Chao-Shen: greater mab <0.0234> (False), greater mse <0.1117> (False)
MLE vs. Miller-Madow: greater mab <0.0621> (False), greater mse <0.1933> (False)
MLE vs. Jackknife: greater mab <0.0572> (False), greater mse <0.1823> (False)
MLE vs. NSB: greater mab <0.1357> (False), greater mse <0.2927> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9441> (False), greater mse <0.9812> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.1881> (False), greater mse <0.3358> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.1691> (False), greater mse <0.3119> (False)
Horvitz-Thompson vs. NSB: greater mab <0.274> (False), greater mse <0.416> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.1877> (False), greater mse <0.3302> (False)
Chao-Shen vs. Jackknife: greater mab <0.1593> (False), greater mse <0.3039> (False)
Chao-Shen vs. NSB: greater mab <0.2759> (False), greater mse <0.4108> (False)
Miller-Madow vs. Jackknife: greater mab <0.0328> (False), greater mse <0.1287> (False)
Miller-Madow vs. NSB: greater mab <0.6185> (False), greater mse <0.643> (False)
Jackknife vs. NSB: greater mab <0.7029> (False), greater mse <0.6927> (False)


N=10000, K=5
MLE: bias <-8.700908690301046e-06>, mab <0.004983622307315511, mse <4.312236473289978e-05>
Horvitz-Thompson: bias <-6.7214589627632715e-06>, mab <0.004982910045987336, mse <4.311895294090499e-05>
Chao-Shen: bias <-6.703702943998191e-06>, mab <0.004982913246697747, mse <4.311916540015359e-05>
Miller-Madow: bias <0.00019129909130967691>, mab <0.0049890583535136266, mse <4.315888436942363e-05>
Jackknife: bias <0.0001916587184047999>, mab <0.004989044240882803, mse <4.315923611097639e-05>
NSB: bias <0.00024792757378870394>, mab <0.004992022265874877, mse <4.3191025037873264e-05>
MLE vs. Horvitz-Thompson: greater mab <0.2259> (False), greater mse <0.4461> (False)
MLE vs. Chao-Shen: greater mab <0.2327> (False), greater mse <0.4523> (False)
MLE vs. Miller-Madow: greater mab <0.8065> (False), greater mse <0.669> (False)
MLE vs. Jackknife: greater mab <0.804> (False), greater mse <0.6655> (False)
MLE vs. NSB: greater mab <0.8534> (False), greater mse <0.7346> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.4999> (False), greater mse <0.7479> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.8291> (False), greater mse <0.6766> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.8377> (False), greater mse <0.6804> (False)
Horvitz-Thompson vs. NSB: greater mab <0.8736> (False), greater mse <0.7469> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.8357> (False), greater mse <0.6788> (False)
Chao-Shen vs. Jackknife: greater mab <0.8297> (False), greater mse <0.6775> (False)
Chao-Shen vs. NSB: greater mab <0.8732> (False), greater mse <0.748> (False)
Miller-Madow vs. Jackknife: greater mab <0.3885> (False), greater mse <0.5332> (False)
Miller-Madow vs. NSB: greater mab <0.9503> (False), greater mse <0.8939> (False)
Jackknife vs. NSB: greater mab <0.9481> (False), greater mse <0.8826> (False)


alpha = 0.0033333333333333335
N=10, K=10
MLE: bias <-0.429158715292001>, mab <0.43190088292193096, mse <0.2367325969541404>
Horvitz-Thompson: bias <-0.034859686368634124>, mab <0.29458418846580914, mse <0.13504692878866173>
Chao-Shen: bias <-0.010587343085207167>, mab <0.3062725824323592, mse <0.15034591746054748>
Miller-Madow: bias <-0.21365871529200123>, mab <0.2758923270117497, mse <0.12150287551553961>
Jackknife: bias <-0.05758157154365851>, mab <0.2645096324811759, mse <0.11093892466771293>
NSB: bias <0.2951830075169701>, mab <0.4268530132879235, mse <0.3042461095447725>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.3815> (False), greater mse <0.9996> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0014> (True), greater mse <0.0007> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.0002> (True), greater mse <0.0001> (True)
Chao-Shen vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0102> (False), greater mse <0.0003> (True)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=100, K=10
MLE: bias <-0.04546143137930102>, mab <0.06943652532325938, mse <0.007778698143515021>
Horvitz-Thompson: bias <-0.01134112119180428>, mab <0.05890586338087166, mse <0.005690292500475771>
Chao-Shen: bias <-0.01711681889758421>, mab <0.05908592839031419, mse <0.005756467121069213>
Miller-Madow: bias <-0.004381431379301041>, mab <0.060504370851701114, mse <0.005944727906713418>
Jackknife: bias <0.001994388628562803>, mab <0.060131260866880844, mse <0.005857691203752327>
NSB: bias <0.0170679206286205>, mab <0.06214839485308426, mse <0.006161509469152631>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.7588> (False), greater mse <0.9507> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9952> (False), greater mse <0.9949> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.9719> (False), greater mse <0.9581> (False)
Horvitz-Thompson vs. NSB: greater mab <0.9996> (True), greater mse <0.9991> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9886> (False), greater mse <0.9769> (False)
Chao-Shen vs. Jackknife: greater mab <0.9391> (False), greater mse <0.8387> (False)
Chao-Shen vs. NSB: greater mab <0.9983> (True), greater mse <0.991> (False)
Miller-Madow vs. Jackknife: greater mab <0.0533> (False), greater mse <0.0104> (False)
Miller-Madow vs. NSB: greater mab <0.9934> (False), greater mse <0.9771> (False)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=1000, K=10
MLE: bias <-0.004393548865461135>, mab <0.018619946817379305, mse <0.0005729256685403385>
Horvitz-Thompson: bias <-0.003680759646005722>, mab <0.01849379318559918, mse <0.0005649915605539621>
Chao-Shen: bias <-0.0037583507499917156>, mab <0.01850324885663155, mse <0.0005655834169763631>
Miller-Madow: bias <6.995113453888968e-05>, mab <0.018305249989675067, mse <0.0005537708793066305>
Jackknife: bias <0.0001796906089694743>, mab <0.0182993587789654, mse <0.0005532760457563055>
NSB: bias <0.0006558504495869264>, mab <0.018288253188030117, mse <0.0005522640333711536>
MLE vs. Horvitz-Thompson: greater mab <0.0033> (True), greater mse <0.0009> (True)
MLE vs. Chao-Shen: greater mab <0.0019> (True), greater mse <0.0006> (True)
MLE vs. Miller-Madow: greater mab <0.0095> (False), greater mse <0.002> (True)
MLE vs. Jackknife: greater mab <0.0113> (False), greater mse <0.0029> (True)
MLE vs. NSB: greater mab <0.0152> (False), greater mse <0.0038> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.875> (False), greater mse <0.9395> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0651> (False), greater mse <0.028> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.0535> (False), greater mse <0.0257> (False)
Horvitz-Thompson vs. NSB: greater mab <0.0648> (False), greater mse <0.0293> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.0527> (False), greater mse <0.0208> (False)
Chao-Shen vs. Jackknife: greater mab <0.0489> (False), greater mse <0.0185> (False)
Chao-Shen vs. NSB: greater mab <0.0612> (False), greater mse <0.0218> (False)
Miller-Madow vs. Jackknife: greater mab <0.16> (False), greater mse <0.0531> (False)
Miller-Madow vs. NSB: greater mab <0.2006> (False), greater mse <0.089> (False)
Jackknife vs. NSB: greater mab <0.2627> (False), greater mse <0.1404> (False)


N=10000, K=10
MLE: bias <-0.00041598127789435943>, mab <0.005829269293771395, mse <5.456117402841645e-05>
Horvitz-Thompson: bias <-0.0004051147405865538>, mab <0.0058290679560557826, mse <5.454005491937595e-05>
Chao-Shen: bias <-0.0004061026873404476>, mab <0.005829033233993043, mse <5.453971913352183e-05>
Miller-Madow: bias <3.3768722105621316e-05>, mab <0.005820798009307596, mse <5.4390857375711584e-05>
Jackknife: bias <3.534613438200052e-05>, mab <0.005820755042164038, mse <5.4389306808385146e-05>
NSB: bias <5.531343593982374e-05>, mab <0.0058196045784315855, mse <5.4365104866794595e-05>
MLE vs. Horvitz-Thompson: greater mab <0.4552> (False), greater mse <0.2596> (False)
MLE vs. Chao-Shen: greater mab <0.4506> (False), greater mse <0.2291> (False)
MLE vs. Miller-Madow: greater mab <0.271> (False), greater mse <0.2084> (False)
MLE vs. Jackknife: greater mab <0.2732> (False), greater mse <0.2041> (False)
MLE vs. NSB: greater mab <0.2579> (False), greater mse <0.1937> (False)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.4538> (False), greater mse <0.4793> (False)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.276> (False), greater mse <0.2377> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.2664> (False), greater mse <0.2249> (False)
Horvitz-Thompson vs. NSB: greater mab <0.2552> (False), greater mse <0.2135> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.2866> (False), greater mse <0.2425> (False)
Chao-Shen vs. Jackknife: greater mab <0.2773> (False), greater mse <0.2342> (False)
Chao-Shen vs. NSB: greater mab <0.2516> (False), greater mse <0.212> (False)
Miller-Madow vs. Jackknife: greater mab <0.4152> (False), greater mse <0.3037> (False)
Miller-Madow vs. NSB: greater mab <0.1024> (False), greater mse <0.0838> (False)
Jackknife vs. NSB: greater mab <0.1027> (False), greater mse <0.093> (False)


alpha = 0.0033333333333333335
N=10, K=100
MLE: bias <-1.994717449492089>, mab <1.994717449492089, mse <3.994489593639471>
Horvitz-Thompson: bias <-0.9263899706659632>, mab <0.9263899706659632, mse <0.9378797811834919>
Chao-Shen: bias <-0.6559898009333112>, mab <0.6559898009333112, mse <0.526270224159029>
Miller-Madow: bias <-1.5849174494920912>, mab <1.5849174494920912, mse <2.538442160110814>
Jackknife: bias <-1.1562944240391133>, mab <1.1562944240391133, mse <1.3895099547886025>
NSB: bias <-0.6915247797490549>, mab <1.14101546271148, mse <1.7178457955227433>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Jackknife vs. NSB: greater mab <0.2827> (False), greater mse <0.9999> (True)


N=100, K=100
MLE: bias <-0.4645192329223063>, mab <0.4645192329223063, mse <0.22273499746819417>
Horvitz-Thompson: bias <0.39266232621491387>, mab <0.3946764880072264, mse <0.1850338326923341>
Chao-Shen: bias <-0.04967886662078064>, mab <0.10504226153448029, mse <0.017906007876527394>
Miller-Madow: bias <-0.21877923292230575>, mab <0.21955937285696095, mse <0.05742773218790777>
Jackknife: bias <-0.07291037212804027>, mab <0.10551122875749457, mse <0.01794058089384647>
NSB: bias <0.13390212608442212>, mab <0.1614800048407998, mse <0.03828200405320902>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Jackknife: greater mab <0.6805> (False), greater mse <0.5501> (False)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=1000, K=100
MLE: bias <-0.050207442732998396>, mab <0.050703384678674246, mse <0.003258216531284713>
Horvitz-Thompson: bias <0.007988314446658925>, mab <0.023477930922790456, mse <0.0008630818504106438>
Chao-Shen: bias <-0.017325012400480358>, mab <0.025974464496209233, mse <0.0010337189957877646>
Miller-Madow: bias <-0.005243942732998364>, mab <0.022554976723703837, mse <0.0007919390835458317>
Jackknife: bias <0.0015657777765768425>, mab <0.022210772108521244, mse <0.0007654556600722085>
NSB: bias <0.010471984566484717>, mab <0.023770876018160355, mse <0.0008715770569488503>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9996> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0241> (False), greater mse <0.009> (False)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.86> (False), greater mse <0.7051> (False)
Chao-Shen vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. NSB: greater mab <0.0013> (True), greater mse <0.0004> (True)
Miller-Madow vs. Jackknife: greater mab <0.0539> (False), greater mse <0.0146> (False)
Miller-Madow vs. NSB: greater mab <0.9965> (False), greater mse <0.9982> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=10000, K=100
MLE: bias <-0.004833161471065391>, mab <0.0074838035779299875, mse <8.568345877983632e-05>
Horvitz-Thompson: bias <-0.0038270917917883956>, mab <0.007095815888743569, mse <7.739260377593495e-05>
Chao-Shen: bias <-0.004133963693953966>, mab <0.007195761270087751, mse <7.95386399378172e-05>
Miller-Madow: bias <6.283852893472108e-05>, mab <0.006259951287440206, mse <6.241110588980639e-05>
Jackknife: bias <0.0001775705726577721>, mab <0.0062610301177014865, mse <6.244619419928589e-05>
NSB: bias <0.00014413076102385203>, mab <0.006253488479188645, mse <6.229814500904202e-05>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. Jackknife: greater mab <0.6094> (False), greater mse <0.7067> (False)
Miller-Madow vs. NSB: greater mab <0.0536> (False), greater mse <0.0507> (False)
Jackknife vs. NSB: greater mab <0.0081> (False), greater mse <0.0008> (True)


alpha = 0.0033333333333333335
N=10, K=1000
MLE: bias <-4.198367912555834>, mab <4.198367912555834, mse <17.62886124538049>
Horvitz-Thompson: bias <-2.989072404494847>, mab <2.989072404494847, mse <8.948748226676777>
Chao-Shen: bias <-2.927530181147656>, mab <2.927530181147656, mse <8.579219479116865>
Miller-Madow: bias <-3.7540179125558333>, mab <3.7540179125558333, mse <14.09713550714771>
Jackknife: bias <-3.265720438301342>, mab <3.265720438301342, mse <10.674165044940144>
NSB: bias <-3.9317741632920704>, mab <3.9317741632920704, mse <16.004966527178475>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=100, K=1000
MLE: bias <-2.0101411035489747>, mab <2.0101411035489747, mse <4.042812645535008>
Horvitz-Thompson: bias <0.28339449366472685>, mab <0.2914251491120457, mse <0.10582531192218007>
Chao-Shen: bias <-0.1511804868501707>, mab <0.32376976325565493, mse <0.16174165088592174>
Miller-Madow: bias <-1.5603311035489784>, mab <1.5603311035489784, mse <2.438247072380052>
Jackknife: bias <-1.1375032053266902>, mab <1.1375032053266902, mse <1.3008545143364054>
NSB: bias <0.455833241699781>, mab <0.51203296275922, mse <0.41888133545211326>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.9991> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Horvitz-Thompson vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Jackknife vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)


N=1000, K=1000
MLE: bias <-0.46773281708771963>, mab <0.46773281708771963, mse <0.21947485816775417>
Horvitz-Thompson: bias <0.8542175653540072>, mab <0.8542175653540072, mse <0.7350455583400299>
Chao-Shen: bias <-0.057351360903909146>, mab <0.061229364880316446, mse <0.0051077567002984796>
Miller-Madow: bias <-0.21786231708771994>, mab <0.21786231708771994, mse <0.048428937831702185>
Jackknife: bias <-0.07177894547549817>, mab <0.07231647202315167, mse <0.006428448090526497>
NSB: bias <0.12728997948994858>, mab <0.1273897213592394, mse <0.0182456073467035>
MLE vs. Horvitz-Thompson: greater mab <0.9999> (True), greater mse <0.9999> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. Jackknife: greater mab <0.9999> (True), greater mse <0.9999> (True)
Chao-Shen vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)


N=10000, K=1000
MLE: bias <-0.05156726717034863>, mab <0.05156726717034863, mse <0.002733333459690284>
Horvitz-Thompson: bias <0.02757082703713103>, mab <0.02757082703713103, mse <0.0008438517134540093>
Chao-Shen: bias <-0.016512119019913563>, mab <0.016732247734220565, mse <0.0003458244992849723>
Miller-Madow: bias <-0.00614526717034862>, mab <0.008631493391005279, mse <0.00011433988498766356>
Jackknife: bias <0.000661805802163367>, mab <0.006979029194429846, mse <7.655276953918308e-05>
NSB: bias <0.009196966526610268>, mab <0.010448204024324418, mse <0.0001602780473546845>
MLE vs. Horvitz-Thompson: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
MLE vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Chao-Shen: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Horvitz-Thompson vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Miller-Madow: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Chao-Shen vs. NSB: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. Jackknife: greater mab <0.0001> (True), greater mse <0.0001> (True)
Miller-Madow vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)
Jackknife vs. NSB: greater mab <0.9999> (True), greater mse <0.9999> (True)