Title
Rank Regression in Ranked-Set Samples
Speaker
Omer Ozturk, Department of Statistics, The Ohio State University
Abstract
The use of statistical methods based on ranked-set sampling can lead to a substantial improvement over analog methods associated with the simple random sampling schemes. In this talk, I will discuss a rank-based estimator and three testing procedures for multiple linear regression models for the 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 it has higher Pitman asymptotic efficiency than the simple random sample rank regression estimator. I will also introduce three testing procedures in order to test a general linear hypothesis. Testing procedures include dispersion, Wald and aligned-rank test. It is shown that all these test statistics converge to a chi-square distribution and the aligned-rank test reduces to the simple random sample analog of the Kruskal-Wallis test for one way analysis of variance.
Under the assumption of a perfect judgment ranking, I will construct an optimal allocation design of order statistics for set sizes less than seven. The optimal allocation design quantifies middle observation(s) for symmetric unimodal distributions and smallest (largest) observation for right (left) skewed distributions. I will present an example to illustrate the use of the proposed procedure.
