Least square estimators in multiple linear regressions under multicollinearity become unstable as they produce large variance for the estimated regression coefficients. Hoerl and Kennard 1970, developed ridge estimators for cases of high degree of collinearity. In ridge estimation, the estimation of ridge parameter ( k ) is vital. In this article new methods for estimating ridge parameter are introduced. The performance of the proposed estimators is investigated through mean square errors (MSE). Monte-Carlo simulation technique indicated that the proposed estimators perform better than ordinary least squares (OLS) estimators as well as few other ridge estimators.
Presence of collinearity among the explanatory variables results in larger standard errors of parameters estimated. When multicollinearity is present among the explanatory variables the ordinary least square (OLS) estimators tend to be unstable due to larger variance of the estimators of the regression coefficients. As alternatives to OLS estimators few ridge estimators are available in the literature. This paper presents some of the popular ridge estimators and attempts to provide (i) a generalized class of ridge estimators and (ii) a modified ridge estimator. The performance of the proposed estimators is investigated with the help of Monte-Carlo simulation technique. Simulation results indicate that the suggested estimators perform better than the ordinary least square (OLS) estimators and other estimators considered in this paper.
Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indicates that the performance of the suggested estimators is slightly better and more stable with respect to degree of multicollinearity, sample size, and error variance.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.