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

Abstract

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(d 1 , d 2 ,. .. , d p), 0 < d i < 1, i = 1,. .. , p. We support our findings by some numerical illustrations.

Jackknifed Liu-type Estimator in Poisson Regression Model

“…The most popular biased estimator is Karbalaee et al (2019) which adopts the Poisson regression model and is defined as follows Algamal ( 2018), Arashi et al (2014) and Arashi et al (2017)…”

“…The six explanatory variables considerable are the number of yellow cards (x 1 ), the number of red cards (x 2 ), the total number of substitutions (x 3 ), the number of matches with 2.5 goals on average (x 4 ), the number of matches that ended with goals (x 5 ), and the ratio of the goals scoreds to the number of matches (x 6 ). Montgomery et al (2015), Karbalaee et al (2019) and Liu (1993) is used to check whether the Poisson regression model fits these data well or not. The result of the residual deviance test is equal to 7.394 with 14 degrees of freedom and the p-value is 0.916.…”

A new Poisson Liu Regression Estimator: method and application

“…Furthermore, Arashi et al [4,5] deliberated the improved preliminary test and Stein-rule Liu estimators, and Liu type estimator. Recently, Karbalaee et al [11] introduced a Preliminary test generalized Liu estimator with series of stochastic restrictions. However, the literature on the Liu estimator of a generalized linear model is rather limited.…”

“…In recent research, it is a stylized fact that the shrinkage estimators are considered as an efficient remedial measure to combat multicollinearity problem [ 11 , 22 ]. Many researchers propose different type of shrinkage estimators to overcome multicollinearity for different models.…”

“…Recently, Karbalaee et al . [ 11 ] introduced a Preliminary test generalized Liu estimator with series of stochastic restrictions. However, the literature on the Liu estimator of a generalized linear model is rather limited.…”