On the Preliminary Test Generalized Liu Estimator with Series of Stochastic Restrictions

When a series of stochastic restrictions are available, we study the performance of the preliminary test generalized Liu estimators (PTGLEs) based on the Wald, likelihood ratio and Lagrangian multiplier tests. In this respect, the optimal range of the biasing parameter is obtained under the mean square error sense. For this, the minimum/maximum value of the biasing matrix components is used to give the proper optimal range, where the biasing matrix is D=diag(d1,d2,...,dp)‎, 0< i<1‎, i=1,...,p. We support our findings by some numerical illustrations.