Some Shrinkage estimators based on median ranked set sampling

Abstract

In this study, some shrinkage estimators using a median ranked set sample in the presence of multicollinearity were studied. Initially, we constructed the multiple regression model using median ranked set sampling. We also adapted the Ridge and Liu-type estimators to these multiple regression model. To investigate the efficiency of these estimators, a simulation study was performed for a different number of explanatory variables, sample sizes, correlation coefficients, and error variances in perfect and imperfect ranking cases. In addition, these estimators were compared with other estimators that are based on ranked set sample using simulation study. It is shown that when the collinearity is moderate, Ridge estimator using median ranked set sample performs better than other estimators and when the collinearity increases, Liu-type estimator using median ranked set sample gets better than all other estimators do. When the collinearity is smaller than 0.95, ridge estimator based on median ranked set sample is more efficient than Liu-type estimator based on same sample. However, this threshold increases as the sample size increases and the number of explanatory variables decreases. In addition, real data example is presented to illustrate how collinearity affects the estimators under median ranked set sampling and ranked set sampling.