Generalized Ridge Regression: Biased Estimation for Multiple Linear Regression Models

TL;DR

This paper investigates the generalized ridge regression method for multiple linear models with nonorthogonal regressors, analyzing its estimation, mean squared error, goodness of fit, and bootstrap inference to improve econometric modeling.

Contribution

It provides a comprehensive analysis of the generalized ridge regression, including estimation procedures and inference methods, which were previously underexplored.

Findings

Derived formulas for mean squared error of the estimator

Evaluated goodness of fit for the generalized ridge regression

Developed bootstrap inference techniques for the model

Abstract

When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most commonly used alternative; however, its generalized version has hardly been analyzed. The present work addresses the estimation of this generalized version, as well as the calculation of its mean squared error, goodness of fit and bootstrap inference.