Weighted Estimation of Quantiles Using Unbalanced Ranked Set Sampling

Abstract HeIn the case where the population distribution is unknown, the nonparametric weighted estimation of quantiles under unbalanced ranked set sampling is proposed because observations with different ranks are not identically distributed. It is shown analytically the optimal weighted version always improves the efficiency for all distributions whether ranking is perfect or not. Then, the sampling allocation that maximizes the estimation efficiency is identified and shown to not depend on the population distribution. Finally, results of computed relative efficiencies and an application to a real data set are presented to illustrate some of the theoretical findings.

[1]  Bimal K. Sinha,et al.  Ranked Set Sampling: Theory and Applications , 2003 .

[2]  Min Zhu.  Quantile Estimation from Ranked Set Sampling Data , 2005 .

[3]  Jeff Terpstra,et al.  Optimal rank set sampling estimates for a population proportion , 2005 .

[4]  Thomas P. Hettmansperger.  The ranked-set sample sign test , 1995 .

[5]  S. Stokes,et al.  Estimation of Variance Using Judgment Ordered Ranked Set Samples , 1980 .

[6]  Stephen L. Rathbun,et al.  The Population Dynamics of a Long-Lived Conifer (Pinus palustris) , 1988, The American Naturalist.

[7]  Zehua Chen.  Density estimation using ranked-set sampling data , 2004, Environmental and Ecological Statistics.

[8]  G. McIntyre,et al.  A method for unbiased selective sampling, using ranked sets , 1952 .

[9]  Ganapati P. Patil,et al.  Ranked set sample sign test for quantiles , 2002 .

[10]  Brett Presnell,et al.  U-Statistics and imperfect ranking in ranked set sampling , 1999 .

[11]  D S Bhoj.  Ranked set sampling with unequal samples. , 2001, Biometrics.

[12]  Lirong Cui,et al.  A Further Study on Reliable Life Estimation under Ranked Set Sampling , 2012 .

[13]  Lirong Cui,et al.  Optimal sign test for quantiles in ranked set samples , 2010 .

[14]  Narayanaswamy Balakrishnan,et al.  Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples , 2006 .

[15]  T. Sager,et al.  Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions , 1988 .

[16]  Douglas A. Wolfe,et al.  The Effect of Imperfect Judgment Rankings on Properties of Procedures Based on the Ranked-Set Samples Analog of the Mann-Whitney-Wilcoxon Statistic , 1994 .

[17]  Francisco J. Samaniego,et al.  Nonparametric Maximum Likelihood Estimation Based on Ranked Set Samples , 1994 .

[18]  Douglas A. Wolfe.  Ranked set sampling: An approach to more efficient data collection , 2004 .

[19]  THE OPTIMAL RANKED-SET SAMPLING SCHEME FOR INFERENCE ON POPULATION QUANTILES , 2003 .