## Brazilian Journal of Probability and Statistics

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

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

Hani M. Samawi and Mavis Pararai

#### 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 31 December 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1262271213

**Digital Object Identifier**

doi:10.1214/08-BJPS010

**Mathematical Reviews number (MathSciNet)**

MR2751607

**Zentralblatt MATH identifier**

1298.62070

**Keywords**

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

#### Citation

Samawi, Hani M.; Pararai, Mavis. On the optimality of bivariate ranked set sample design for the matched pairs sign test. Braz. J. Probab. Stat. 24 (2010), no. 1, 24--41. doi:10.1214/08-BJPS010. https://projecteuclid.org/euclid.bjps/1262271213