26 10 Vol.26 No.10 Statistics&InformationForum 2011 10 Oct.2011 ab b ( a. ;b. 100872) ; ; ; C811 A 1007-3116(2011)10-0003-06 1934 Neyman Neyman [1] 2011-05-23 (10JJD790036); (11BTJ009) ; 3
[2] y π π ( )π j πj i πi πj i 2. U = {1 K N} y p(s) S i j k I k yij wi = 1 πi πj i I k = 1 k S ^tπ = { i j wiyij 0k S y S πk k πk = Pr(k S)=Pr(I k =1)= p(s) k S T = U yk π V(^tπ )=V( s ) yk)= U Δkl ) yk ) yl (2) 1.π Δkl =πkl-πkπlπkl k l πkl <πkπl ) yk =yk/πk ) yl =yl/πl k l Uπkl >0 V(^tπ ) 2. π ^V(^tπ )=^V( s ) yk)= S ) Δkl ) yk ) yl (3) ) [3]42-45 Δkl = Δkl/πkl 3. π ( ) π ) p(s) i πi ^tπ = U Ik yk yk = (1) S πk πk y yk y k S [4] π ( ) Horvitz- Thompson Y 1/πk yk 1/πk 4 4. ( 1.
5. Y = Y i + π i S Y i (5) i S S Cassel S rndal Wret- man 珔 x 1N-n = (N -n) -1 (N 珔 x N - i ) i Sx 珚 [3]42-45 Y N 珚 Y reg = N -1^Y (7) 珚 Y reg AV( 珚 Y reg - 珚 Y N )= E{E[( 珚 Y reg - 珚 Y N ) 2 F N ]}- ( ) 1. y 2. y y 0 σ 2 3. ( ) N ( ) 1. yi 烄 =x iβ+e i 烅烆 e i ~ind(0γiσ 2 )(i=1 N ) yi x i (k+1) x i = (1x i1 x i2 x ik ) β = ( β 0 β 1 β k) e i i je i x i β X [5]183-184 ^β = (X D γ -1 X) -1 X D γ -1 y (4) X = (x 1 x 2 x n ) D γ =diag(γ11γ22 γnn)y = (y1y2 yn) n S Y ^Y = i Syi + i S yi = i S yi + (N -n) 珔 x 1N-n^β (6) [E{E[( 珚 Y reg - 珚 Y N ) F N ]}] 2 (8) 2. 3. 5
[12] [6]2-4 4. Sugden Smith [13] Pfefermann [14] Kot [15] ; Sterba 1 [4] Kot Demets Halperin Nathan Holt Hausman Wise Jewel 1. Y Y = Xβ +ε β ^β = [7-8][9]366-391[10] Skinner Holt Smith (X X) X y ^β = (X WX) X Wy W [11]146-147 Pfef- 2. fermann Pfef- fermann Skinner Holmes Goldstein Rasbash Kovacevic Rai Rabe - Hesketh Skrondal [16-18] 3. 1 6 p(s)
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26 10 Vol.26 No.10 Statistics&InformationForum 2011 10 Oct.2011 ( 730000) ; ; ; ; C812 O212 A 1007-3116(2011)10-0008-08 1922 (The MakingofIndex Num- ber) (Fisher) 2011-06-08 ; AComparativeStudyofComplexSamplingInferenceSystems JIN Yong-jin ab HEBen-lan b (a.appliedstatisticalscienceresearchcenter; b.schoolofstatisticsrenminuniversityofchinabeijing100872china) AbstractThereareusualytwoinferencesystemsforcomplexsampletraditionalstatisticalinference andmodel-basedstatisticalinference.traditionalsamplingtheorybasedonrandomizationtheorybelieved thatthevaluesofvariablesonpopulationunitsarefixedandtherandomnessembodiesinsampleselection. Itsinferenceforpopulationdependsonsamplingdesign.Estimatorsofthismethodarerobustwhensample sizeislargebutineficiency whensamplesizeissmalandthereare missingdata.anotherdeduction basedon modelthinksthatthefinitepopulationisarandom sampledrawnfrom asuper-population. Inferenceforpopulationdependsonmodelingbutestimatorsofthisinferencesystemarebiasedundernon -ignorablesamplescheme.basedontheanalysisofthecorecontentsofthetwo methodsthispaper proposessamplingscheme-assistedand model-basedinferenceandpointsoutthatthis methodhas importantapplicationvalueincomplexsampling. Keywordsrandomization-based;model-based;samplingscheme;complexsamplinginference ( ) 8