The Performance of a Ridge Estimator Based on Harmonic Mean

Satish Bhat¹ , R. Vidya²

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.4 , pp.70-76, Aug-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.7076

Online published on Aug 31, 2019

Copyright © Satish Bhat, R. Vidya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Linear dependence between predictors is one of the serious issues in regression analysis. Due to near linear dependence (or multicollinearity) between any two or more predictors, ordinary least squares (OLS) method will yield unstable estimates to the regression coefficients. In the literature, several techniques like Ridge regression, Principal component regression, Partial least squares regression, Liu method of regression etc., have been developed to overcome problem of multicollinearity. Among them Ridge regression is one of the most widely used methods, which will yield more stable estimate’s as compared to OLS estimator. Here we propose a new ridge estimator based on Harmonic mean method. Performance of the ridge estimators is evaluated both theoretically and empirically under a wide range of degree of multicollinearity and error variances. Both methods have indicated that the performance of the suggested estimator is slightly more stable than some existing estimators, which are considered under study with respect to various degrees of multicollinearity, sample size, and error variance.

Key-Words / Index Term :
Multiple linear regression (MLR), Multicollinearity, Ridge regression, and MSE

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