Shrinkage Estimation Strategies in Generalized Ridge Regression Models Under Low/High-Dimension Regime

TL;DR

This paper introduces new shrinkage estimation methods based on generalized ridge regression suitable for high-dimensional and low-sample-size problems, with theoretical analysis and empirical validation showing competitive performance.

Contribution

It proposes novel shrinkage estimators within generalized ridge regression applicable to both low and high-dimensional settings, with theoretical properties and empirical comparisons.

Findings

Proposed estimators perform well in simulations.

Methods outperform some existing penalty techniques.

Theoretical properties are established for different regimes.

Abstract

In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also, it is obtained theoretical properties of the proposed estimators for Low/High Dimensional cases. Furthermore, the performance of the listed estimators is demonstrated by both simulation studies and real-data analysis, and compare its performance with existing penalty methods. We show that the proposed methods compare well to competing regularization techniques.