Abstract
In ranked-set sampling (RSS) and judgment post-stratification (JPS), more efficient inference is obtained by creating a stratification based on ranking information. Using this stratification exactly as is done in stratified sampling or standard post-stratification leads to the standard nonparametric estimators for RSS and JPS. However, we show that strata obtained from ranking information satisfy additional constraints that need not be met by ordinary strata. Specifically, the in-stratum cumulative distribution functions (CDFs) can be no more extreme, in a certain sense, than the CDFs for order statistics from the overall distribution. The additional constraints can be used to obtain better small-sample estimates of the in-stratum CDFs using either RSS or JPS. In the JPS case, the constraints also lead to better small-sample estimates of the overall CDF and the population mean.
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References
Barnett V., Moore K. (1997) Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering. Journal of Applied Statistics 24: 697–710
Bohn L.L., Wolfe D.A. (1994) The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analogue of the Mann–Whitney–Wilcoxon statistic. Journal of the American Statistical Association 89: 168–176
Du J., MacEachern S. (2008) Judgement post-stratification for designed experiments. Biometrics 64: 345–354
Fligner M.A., MacEachern S.N. (2006) Nonparametric two-sample methods for ranked-set sample data. Journal of the American Statistical Association 101: 1107–1118
Lohr S. (1999) Sampling: design and analysis. Pacific Grove, CA, Duxbury
MacEachern S.N., Ozturk O., Wolfe D.A., Stark G.A. (2002) A new ranked set sample estimator of variance. Journal of the Royal Statistical Society, Series B 64: 177–188
MacEachern S.N., Stasny E.A., Wolfe D.A. (2004) Judgement post-stratification with imprecise rankings. Biometrics 60: 207–215
McIntyre G.A. (1952) A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3: 385–390
McIntyre, G. A. (2005). A method for unbiased selective sampling, using ranked sets. The American Statistician, 59, 230–232 (originally appeared in Australian Journal of Agricultural Research, 3, 385–390).
Ozturk O. (2007) Statistical inference under a stochastic ordering constraint in ranked set sampling. Journal of Nonparametric Statistics 19: 131–144
Ridout M.S., Cobby J.M. (1987) Ranked set sampling with non-random selection of sets and errors in ranking. Applied Statistics 36: 145–152
StatLib Datasets Archive. (2009). Bodyfat dataset. Available at http://lib.stat.cmu.edu/datasets
Stokes S.L. (1995) Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47: 465–482
Stokes S.L., Sager T.W. (1988) Characterization of a ranked-set sample with application to estimating distribution functions. Journal of the American Statistical Association 83: 374–381
Wang X., Lim J., Stokes L. (2008) A nonparametric mean estimator for judgment poststratified data. Biometrics 64: 355–363
Ziegler G.M. (1995) Lectures on polytopes. Springer, New York
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Frey, J., Ozturk, O. Constrained estimation using judgment post-stratification. Ann Inst Stat Math 63, 769–789 (2011). https://doi.org/10.1007/s10463-009-0255-z
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DOI: https://doi.org/10.1007/s10463-009-0255-z