On regression analysis using bivariate ranked set samples

Ranked set samples are recently introduced in the literature for estimating the population mean and other parameters of interest, ranking only on one of the variables under the study. Bivariate ranked set sampling (BVRSS) was introduced by Al-Saleh and Zheng (2002), for multiple characteristics estimation, based on ranking on two or more variable, under the study, simultaneously. In this paper, BVRSS is considered for regression analysis. Its effect on regression analysis, when the regressors are assumed to be random, is investigated. In particular, parameter estimation, testing hypothesis of the simple regression model fit and residual analysis are studied. It is shown that BVRSS give unbiased and more efficient estimators of the regression model parameters than those obtained based on bivariate simple random sample (BVSRS) and on the ordinary ranked set sample (RSS), using the same number of quantified units. Some inferences based on asymptotic results are given. Numerical comparison using simulation is used to compare the efficiency of the estimators. It appears that using BVRSS increases the precision of regression analysis. Also, it is argued, by using real data, that all residual analysis methods for model diagnostics are still valid when using these samples. Finally, it is believed that this analysis can be extended in straight forward way to multiple regression problems.