A new ridge‐type estimator for the linear regression model with correlated regressors

Abstract

The ridge-type regression estimators are frequently being used to address multicollinearity in the linear regression model due to the inefficiency of the famous ordinary least squares estimator. The ridge-type regression estimator can be in one or two-parameter form. This paper proposes another ridge-type estimator, a two-parameter ridge-type estimator, and establishes its statistical properties theoretically and through Monte Carlo simulation studies. Two different biasing parameters (k 1 d 1 and k 2 d 2 ) were considered for the proposed and compared with six other existing estimators. Results of Monte Carlo simulation studies show the dominance of the proposed method over some existing ones using the mean squared criterion. In addition, the proposed dominated the existing estimators when applied to real-life datasets using mean squared error and cross-validation as the criterion.

A Modified Two Parameter Estimator with Different Forms of Biasing Parameters in the Linear Regression Model

“…Consequently, the proposed modified two-parameter is a general estimator that includes OLS, the Ridge estimator, and the two-parameter estimator proposed by Owolabi et al [17], as seen in cases 1, 2, and 3, respectively.…”

“…Following Owolabi et al [17] and Swindel [5], the proposed estimator with prior information is as follows:…”

“…Other authors who have discussed the biasing parameter of the Liu estimator are Akdeniz and Kaciranlar [25], Kaciranlar [26], Alheety and Kibria [27], Shukur et al [28] and Qasim, Amin, and Ullah [29], Månsson et al [30]. This study adopts the biasing parameters k and d used by Owolabi et al [17] k…”

“…Some two-parameter estimators that have been proposed in works of literature include Ozkale and Kac ¸iranlar [9]; Yang and Chang [10]; Dorugade [11], Roozbeh [12]; Ayinde et al [13]; Lukman et al [14], Dawoud and Kibria [15], Oladapo et al [16] and more recently Owolabi et al [17][18]. This article proposes a new estimator with prior information, and its properties are derived.…”

On the biased Two-Parameter Estimator to Combat Multicollinearity in Linear Regression Model

“…For practical use, there is a need to estimate the parameters k and d. Different researchers have proposed different estimators of k and d for different types of regression models. Following some of these researchers like Hoerl et al [7], Liu [8], Lukman and Ayinde [23], Ayinde et al [24], Owolabi et al [25]. and Dawoud et al [12,26] to mention a few, among others.…”