Quantile inference based on partially rank-ordered set samples

Abstract This paper develops statistical inference for population quantiles based on a partially rank-ordered set (PROS) sample design. A PROS sample design is similar to a ranked set sample with some clear differences. This design first creates partially rank-ordered subsets by allowing ties whenever the units in a set cannot be ranked with high confidence. It then selects a unit for full measurement at random from one of these partially rank-ordered subsets. The paper develops a point estimator, confidence interval and hypothesis testing procedure for the population quantile of order p. Exact, as well as asymptotic, distribution of the test statistic is derived. It is shown that the null distribution of the test statistic is distribution-free, and statistical inference is reasonably robust against possible ranking errors in ranking process.

[1]  Douglas A. Wolfe,et al.  Nonparametric Two-Sample Procedures for Ranked-Set Samples Data , 1992 .

[2]  Lucio Barabesi.  The computation of the distribution of the sign test statistic for ranked-set sampling , 1998 .

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

[4]  Steven N. MacEachern,et al.  Nonparametric Two-Sample Methods for Ranked-Set Sample Data , 2006 .

[5]  Douglas A. Wolfe,et al.  Imperfect Ranking Models for Ranked-Set Sampling , 2007 .

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

[7]  J. L. Clutter,et al.  Ranked Set Sampling Theory with Order Statistics Background , 1972 .

[8]  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 .

[9]  Douglas A. Wolfe,et al.  An improved ranked set two-sample Mann-Whitney-Wilcoxon test , 2000 .

[10]  Omer Ozturk.  One- and two-sample sign tests for ranked set sample selective designs , 1999 .

[11]  Omer Ozturk.  Sampling from partially rank-ordered sets , 2010, Environmental and Ecological Statistics.

[12]  Jayant V. Deshpande,et al.  Ranked-set sample nonparametric quantile confidence intervals , 2006 .

[13]  G. McIntyre.  A Method for Unbiased Selective Sampling, Using Ranked Sets , 2005 .

[14]  Omer Ozturk.  Statistical inference under a stochastic ordering constraint in ranked set sampling , 2007 .

[15]  Omer Ozturk.  Inference in the presence of ranking error in ranked set sampling , 2008 .

[16]  Omer Ozturk.  Two-sample inference based on one-sample ranked set sample sign statistics , 1999 .

[17]  Douglas A. Wolfe,et al.  Optimal allocation procedure in ranked set sampling for unimodal and multi-modal distributions , 2004, Environmental and Ecological Statistics.

[18]  Jesse Frey,et al.  New imperfect rankings models for ranked set sampling , 2007 .

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

[20]  Gutti Jogesh Babu,et al.  Sign test for ranked-set sampling , 1996 .

[21]  Omer Ozturk,et al.  Two sample distribution-free inference based on partially rank-ordered set samples , 2012 .

[22]  Zehua Chen.  On ranked-set sample quantiles and their applications , 2000 .

[23]  Jesse Frey,et al.  Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population , 2006, Environmental and Ecological Statistics.