A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model

Abstract

In a multiple linear regression model, the ordinary least squares estimator is inefficient when the multicollinearity problem exists. Many authors have proposed different estimators to overcome the multicollinearity problem for linear regression models. This paper introduces a new regression estimator, called the Dawoud–Kibria estimator, as an alternative to the ordinary least squares estimator. Theory and simulation results show that this estimator performs better than other regression estimators under some conditions, according to the mean squares error criterion. The real-life datasets are used to illustrate the findings of the paper.

Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

“…Extensions of the two-parameter estimators to the area of GLMs have been recently developed; such as Qasim et al [22], Farghali et al [9], Lukman et al [23], Algamal and Abonazel [12], and Abonazel et al [14]. Following the previous works, we introduced the beta version of the two-parameter estimator of Dawoud and Kibria [5] (BDK) as follows:…”

“…-Following Dawoud and Kibria [5], we suggest two different k of the proposed BDK estimator as follows:…”

“…Also, in the case of an estimator with two parameters, Özkale and Kaçiranlar [4] proposed a two-parameter estimator. Very recently, Dawoud and Kibria [5] proposed a new kind of two-parameter estimator called the Dawoud-Kibria (DK) estimator. There are other recent studies regarding the one parameter and two-parameter estimators in LR and GL models, such as Roozbeh et al [6], Lukman et al [7], Arashi et al [8], Farghali et al [9], Lukman et al [10,11], Algamal and Abonazel [12], Akram et al [13], and Abonazel et al [14].…”

Combining principal component and robust ridge estimators in linear regression model with multicollinearity and outlier

“…3 Alternative estimators to the LSE have been introduced in the literature to handle the problem of multicollinearity. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] To mention a few, the ridge estimator (RE) is a popular technique to reduce the influence of multicollinearity in the regression models. 5 The principal component estimator (PCE) is employed to reduce the dimensionality of the estimation problem.…”

Bayesian Spatiotemporal Modeling and Mapping of Infectious Diseases

“…Multicollinearity causes inefficient estimators of the regression parameters (Dawoud and Kibria 2020), whereas misspecification leads to inconsistent and biased estimators (Hayashi et al 2011;Winship and Western 2016). To deal with both issues simultaneously, structural equation modeling (SEM) can be considered (Winship and Western 2016;Zhao et al 2016).…”