A new Liu-type estimator in linear regression model

Abstract

In this paper, we introduce a new Liu-type estimator called modified Liu estimator based on prior information for the vector of parameters in a linear regression model and discuss its properties. Furthermore, we obtain that our new estimator is superior, in the mean square error matrix sense, to the least squares estimator, Liu estimator, ridge estimator and modified ridge estimator. Finally, a numerical example and a Monte Carlo simulation are done to illustrate some of the theoretical results.

Modified ridge‐type estimator to combat multicollinearity: Application to chemical data

“…The parameter values were chosen such that β ′ β=1, which is a common restriction in simulation studies of this type. 3,4,14 Sample sizes 50 and 100 were used. Three different values of σ (1, 5, and 10) were used.…”

Mean Square Error Comparisons of the Alternative Estimators For The Distributed Lag Models

“…The i − th element of matrix B in (4.21) is ridge and modified ridge estimators, respectively, in Liu and Yang [11]. In this section, we show that Almon-Liu estimator is better than Almon-modified Liu estimator according to the MSE criterion.…”

“…In this study, we have compared theoretical performances of Almon-ridge ( γ k ), Liu and Yang [11] showed with the increasing of the levels of multicollinearity, the smse values of ridge, Liu, modified ridge and modified Liu estimators are decreasing in general for the linear regression model. Moreover, they showed that the smse values of these estimators outperformed to the OLS estimator for all cases.…”

The relative efficiency of Liu-type estimator in a partially linear model

“…Our sampling experiment consists of different combinations of k; d and n. In this study, the explanatory variables are generated by the following equation [12,13]:…”