K‐L estimator for the linear mixed models: Computation and simulation

Abstract

This study introduces a new biased estimator called the K-L estimator for the linear mixed model to overcome the effect of multicollinearity. We derived the mean squared error property of the proposed estimator and made a theoretical comparison with other methods. For the assessment of the K-L estimator, we use the mean squared error criterion as a performance evaluation criterion. Moreover, we defined some shrinkage parameters for the proposed estimator. For numerical evaluation, we use a Monte Carlo simulation study and a real example. The result shows the supremacy of the K-L estimator as compared to the available methods under certain conditions. K E Y W O R D SK-L estimator, linear mixed model, multicollinearity, shrinkage parameters 1 where y (n×1) is the vector of response variable and normally distributed with mean X𝛽 and variance 𝜎 2 H such that H = ZGZ ′ + W. The matrix H consists of two components that are used to model heteroscedasticity and correlation: a random effects component ZGZ ′ and a within-group component W. In some applications, the within-group component R is used to directly model the variance-covariance matrix of the data without the need to incorporate random effects in the model to account for dependence among observations. 4 X (n×p) is known design matrix of explanatory variables, Z (n×mq) is a known design matrix, 𝛽 p×1 is a vector of unknown regression parameters of the fixed effects, u (mq×1) is unobservable vector of random effects, and 𝜀 n×1 is the vector of errors. By assumption,

A New Effective Jackknifing Estimator in the Negative Binomial Regression Model

“…In recent years, Kibria and Lukman [24] developed the Kibria-Lukman (KL) estimator, which was found to outperform the ridge and Liu estimators in the linear regression model. Lukman et al [25] proposed a new biased estimator called the KL estimator for linear mixed models. Aladeitan et al [26] proposed a modified KL estimator in the Poisson regression model.…”