Bivariate Sign Test for One-Sample Bivariate Location Model Using Ranked Set Sample

Abstract

In this article, we introduce a bivariate sign test for the one-sample bivariate location model using a bivariate ranked set sample (BVRSS). We show that the proposed test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the non centrality parameter are derived. The asymptotic distribution of the vector of sample median as an estimator of the locations of the bivariate model is introduced. Theoretical and numerical comparisons of the asymptotic efficiency of the BVRSS sign test with respect to the BVSRS sign test are also given.

Keywords:

• Bivariate ranked set sample
• One-sample bivariate location model
• Power of the test
• Ranked set sample
• Sign test

Mathematics Subject Classification:

• 62G10