Rank Regression in Ranked-Set Samples

Abstract

The use of statistical methods based on ranked-set sampling can lead to a substantial improvement over analog methods associated with simple random sampling schemes. This article develops a rank-based estimator and testing procedures for linear models for ranked-set samples. The estimator is defined as the minimizer of the rank dispersion function with Wilcoxon scores. It is shown that the estimator of the regression parameter is asymptotically normal and has higher Pitman asymptotic efficiency than a simple random-sample rank regression estimator. Three testing procedures are developed to test a general linear hypothesis: dispersion, Wald, and aligned rank tests. It is shown that all of these test statistics converge to a chi-squared distribution and the aligned rank test reduces to a simple random-sample analog of Kruskal-Wallis test for one-way analysis of variance. Under the assumption of perfect judgment ranking, optimal allocation of order statistics are constructed for set sizes smaller than 7. The optimal allocation procedures quantify middle observation(s) for symmetric unimodal distributions and smallest (largest) observation for right- (left-) skewed distributions.