The Matched Pairs Sign Test Using Bivariate Ranked Set Sampling Based on Different Ranking Schemes

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Statistical Methodology




Bivariate rank set sample (BVRSS) matched pair sign test is introduced and investigated for different ranking based schemes. We show that this test is asymptotically more efficient and more powerful than its counterpart sign test based on a bivariate simple random sample (BVSRS) for different ranking schemes. The asymptotic null distribution and the efficiency of the test are derived. Pitman’s asymptotic relative efficiency is used to compare the asymptotic performance of the matched pair sign test using BVRSS versus using BVSRS in all ranking cases. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using any ranking scheme of BVRSS for the matched pair sign test is more efficient than using BVSRS.