Comput Stat
DOI 10.1007/s00180-016-0698-7
ORIGINAL PAPER
Tests of perfect judgment ranking using pseudo-samples
Saeid Amiri
1
· Reza Modarres
2
·
Silvelyn Zwanzig
3
Received: 15 December 2015 / Accepted: 7 October 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract Ranked set sampling (RSS) is a sampling approach that can produce
improved statistical inference when the ranking process is perfect. While some infer-
ential RSS methods are robust to imperfect rankings, other methods may fail entirely
or provide less efficiency. We develop a nonparametric procedure to assess whether
the rankings of a given RSS are perfect. We generate pseudo-samples with a known
ranking and use them to compare with the ranking of the given RSS sample. This
is a general approach that can accommodate any type of raking, including perfect
ranking. To generate pseudo-samples, we consider the given sample as the population
and generate a perfect RSS. The test statistics can easily be implemented for balanced
and unbalanced RSS. The proposed tests are compared using Monte Carlo simulation
under different distributions and applied to a real data set.
Keywords Imperfect rankings · Order statistics · Ranked set sampling · Resampling
1 Introduction
The past three decades have witnessed considerable research and success to extend
the seminal idea of McIntyre (1952) to collect a sample only after judgment ranking
of the sampling units. RSS is a two-stage sampling plan where a number of sam-
pling units are first ranked without taking actual measurements at a small cost and,
B Saeid Amiri
saeid.amiri1@gmail.com
1
Department of Natural and Applied Sciences, University of Wisconsin-Green Bay,
Green Bay, WI, USA
2
Department of Statistics, The George Washington University, Washington, DC, USA
3
Department of Mathematics, Uppsala University, Uppsala, Sweden
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