Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model

Recently, Liu (1993) estimator draws an important attention to estimate the regression parameters for an ill-conditioned linear regression model when the vector of errors is distributed according to the law belonging to the class of elliptically contoured distributions (ECDs). This paper proposed some improved Liu type estimators, namely, the unrestricted Liu estimator (ULE), restricted Liu estimator (RLE), preliminary test Liu estimator (PTLE), shrinkage Liu estimator (SLE) and positive rule Liu estimator (PRLE) for estimating the regression parameters β. The performance of the proposed estimators is compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for parameter d and non-centrality parameter Δ are given.