On the optimality of bivariate ranked set sample design for the matched pairs sign test

On the optimality of bivariate ranked set sample design for the matched pairs sign test

Hani M. Samawi and Mavis Pararai

Source: Braz. J. Probab. Stat. Volume 24, Number 1 (2010), 24-41.

Abstract

An optimal alternative bivariate ranked set sample designs for the matched pairs sign test are obtained. Our investigation revealed that the optimal bivariate ranked set sample designs for matched pairs sign test are those with quantifying order statistics with labels {((r+1)/2, (r+1)/2)} when the set size r is odd and {(r/2, r/2), (r/2 + 1, r/2 + 1)} when the set size r is even. The exact null distributions, asymptotic distributions and Pitman efficiencies of those designs are derived. Numerical analysis of the power of the proposed optimal designs is included. An illustration using real data with a bootstrap algorithm for P-value estimation is used.

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Keywords: Bivariate ranked set sample; bootstrap method; power of the test; P-value of the test; Pitman’s relative efficiency; matched pairs sign test

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Permanent link to this document: http://projecteuclid.org/euclid.bjps/1262271213
Digital Object Identifier: doi:10.1214/08-BJPS010
Mathematical Reviews number (MathSciNet): MR2751607

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