Canadian Journal of Statistics

EDF‐based goodness‐of‐fit tests for ranked‐set sampling

Journal Article

Abstract

Parametric statistical procedures based on ranked‐set sampling are sensitive both to departures from the parametric family and to departures from perfect rankings. In this paper, we develop goodness‐of‐fit tests that are sensitive to departures of both types. These tests are modelled on the Kolmogorov–Smirnov and Cramér–von Mises goodness‐of‐fit tests for simple random sampling, and they take advantage of the fact that under perfect rankings, the cumulative distribution functions (CDFs) for the judgment order statistics are deterministic functions of the population CDF. We consider multiple ways of combining information across the judgment strata, and we find that summing or taking the maximum of separate stratum‐by‐stratum test statistics seems to give the best power. We prove that the best of the proposed tests are consistent against all alternatives. The Canadian Journal of Statistics 42: 451–469; 2014 © 2014 Statistical Society of Canada

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