Asymptotic properties of sample quantiles from a finite population

Annals of the Institute of Statistical Mathematics

Volumn 63, Issue 1, 2011, Pages 157-179

  Chatterjee, Arindam ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Asymptotic normality; Bootstrap; Finite population; Quantile estimation; Variance estimation

Indexed keywords

ASYMPTOTIC NORMALITY; BOOTSTRAP; FINITE POPULATION; QUANTILE ESTIMATION; VARIANCE ESTIMATION;

ESTIMATION; SAMPLING;

ASYMPTOTIC ANALYSIS;

EID: 79551686102     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-008-0210-4     Document Type: Article

References (29)

1. R.R. Bahadur 1966 A note on quantiles in large samples The Annals of Mathematical Statistics 37 577 580 0147.18805 10.1214/aoms/1177699450 189095
2. P.J. Bickel D.A. Freedman 1984 Asymptotic normality and the bootstrap in stratified sampling The Annals of Statistics 12 2 470 482 0542.62009 10.1214/aos/1176346500 740906
3. J.G. Booth R.W. Butler P. Hall 1994 Bootstrap methods for finite populations Journal of the American Statistical Association 89 428 1282 1289 0812.62006 10.2307/2290991 1310222
4. R.L. Chambers R. Dunstan 1986 Estimating distribution functions from survey data Biometrika 73 597 604 0614.62005 10.1093/biomet/73.3.597 897851
5. B. Efron 1979 Bootstrap methods: Another look at the jackknife The Annals of Statistics 7 1 1 26 0406.62024 10.1214/aos/1176344552 515681
6. C.A. Francisco W.A. Fuller 1991 Quantile estimation with a complex survey design The Annals of Statistics 19 1 454 469 0787.62011 10.1214/aos/1176347993 1091862
7. M. Ghosh W.C. Parr K. Singh G.J. Babu 1984 A note on bootstrapping the sample median The Annals of Statistics 12 3 1130 1135 0541.62010 10.1214/aos/1176346731 751302
8. Gross, S. T. (1980). Median estimation in sample surveys. In ASA Proceedings of the Section on Survey Research Methods (pp. 181-184).
9. W. Hoeffding 1963 Probability inequalities for sums of bounded random variables Journal of the American Statistical Association 58 13 30 0127.10602 10.2307/2282952 144363
10. C.T. Isaki W.A. Fuller 1982 Survey design under the regression superpopulation model Journal of the American Statistical Association 77 377 89 96 0511.62016 10.2307/2287773 648029
11. J.G. Kovar J.N.K. Rao C.-F.J. Wu 1988 Bootstrap and other methods to measure errors in survey estimates The Canadian Journal of Statistics 16 suppl. 25 45 10.2307/3315214 997120
12. P. Lahiri 2003 On the impact of bootstrap in survey sampling and small-area estimation Statistical Science 18 2 199 210 10.1214/ss/1063994975 2019788 (Pubitemid 37545093)
13. S.N. Lahiri A. Chatterjee 2007 A Berry-Esseen theorem for hypergeometric probabilities under minimal conditions Proceedings of the American Mathematical Society 135 5 1535 1545 1108.60016 10.1090/S0002-9939-07-08676-5 2276664 (electronic)
14. Lahiri, S. N., Chatterjee, A., Maiti, T. (2006). A sub-gaussian berry-esseen theorem for the hypergeometric distribution. preprint available at http://arxiv.org/abs/math/0602276.
15. T.K. Mak A. Kuk 1993 A new method for estimating finite-population quantiles using auxiliary information The Canadian Journal of Statistics 21 29 38 0773.62006 10.2307/3315655 1221854
16. P.J. McCarthy 1965 Stratified sampling and distribution-free confidence intervals for a median Journal of the American Statistical Association 60 772 783 0127.35804 10.2307/2283244
17. D. Nelson G. Meeden 2006 Noninformative nonparametric quantile estimation for simple random samples Journal of Statistical Planning and Inference 136 1 53 67 1078.62029 10.1016/j.jspi.2004.06.001 2207172 (Pubitemid 41472199)
18. J.N.K. Rao C.F.J. Wu 1988 Resampling inference with complex survey data Journal of the American Statistical Association 83 231 241 0654.62015 10.2307/2288945 941020
19. J.N.K. Rao J.G. Kovar H.J. Mantel 1990 On estimating distribution functions and quantiles from survey data using auxiliary information Biometrika 77 365 375 0716.62013 10.1093/biomet/77.2.365 1064809
20. J. Sedransk J. Meyer 1978 Confidence intervals for the quantiles of a finite population: Simple random and stratified simple random sampling Journal of the Royal Statistical Society, Series B, Methodological 40 239 252 0386.62009 517444
21. J. Shao 1994 L-statistics in complex survey problems The Annals of Statistics 22 2 946 967 0807.62007 10.1214/aos/1176325505 1292550
22. J. Shao 2003 Impact of the bootstrap on sample surveys Statistical Science 18 2 191 198 10.1214/ss/1063994974 2019787 (Pubitemid 37545092)
23. J. Shao Y. Chen 1998 Bootstrapping sample quantiles based on complex survey data under hot deck imputation Statistica Sinica 8 1071 1086 1053.62509 1666229
24. J. Shao C.F.J. Wu 1989 A general theory for jackknife variance estimation The Annals of Statistics 17 3 1176 1197 0684.62034 10.1214/aos/1176347263 1186266
25. J. Shao C.-F.J. Wu 1992 Asymptotic properties of the balanced repeated replication method for sample quantiles The Annals of Statistics 20 3 1571 1593 0766.62005 10.1214/aos/1176348785 1186266
26. K. Singh 1981 On the asymptotic accuracy of Efron's bootstrap The Annals of Statistics 9 6 1187 1195 0494.62048 10.1214/aos/1176345636 630102
27. R.R. Sitter 1992 Comparing three bootstrap methods for survey data The Canadian Journal of Statistics 20 135 154 0753.62006 10.2307/3315464 1183077
28. P. Smith J. Sedransk 1983 Lower bounds for confidence coefficients for confidence intervals for finite population quantiles Communications in Statistics, Part A-Theory and Methods 12 1329 1344 0525.62013 10.1080/03610928308828534 706982
29. R.S. Woodruff 1952 Confidence intervals for medians and other position measures Journal of the American Statistical Association 47 635 646 0047.38002 10.2307/2280781 50845