The modified maximum likelihood estimators for the parameters of the regression model under bivariate median ranked set sampling

We derived the modified maximum likelihood (MML) regression type estimators using bivariate median ranked set sampling (MRSS) and conducted an extensive simulation study to compare them with their least squares (LS) counterparts using MRSS and with the MML and LS counterparts using ranked set sampling (RSS). Under normality, the MML estimators using bivariate MRSS are mostly better than the LS estimators using bivariate MRSS in most of the situations, especially when the correlation between the concomitant and primary variables is high. In general, MRSS is superior to RSS in the estimation of the location parameters of the concomitant and primary variables. In the estimation of the other parameters, RSS is superior to MRSS and the MML estimators using RSS are mostly the best estimators of all. For Weibull distribution, the LS estimators using MRSS are mostly better than the MML estimators using MRSS but in general, the MML estimators using RSS are the superior estimators among all, especially for higher cycles. At the end of the study, we give two examples illustrating the procedures and merits of the newly proposed estimators.