Maximum Likelihood Ridge Regression

TL;DR

This paper reviews the development and key practical findings of maximum likelihood ridge regression from 1975 to 2022, emphasizing its importance in shrinkage techniques for regression analysis.

Contribution

It synthesizes and highlights the most important maximum likelihood results in ridge regression across multiple publications over nearly five decades.

Findings

Maximum likelihood estimation under normal distribution is central to ridge regression.

Practical applications of shrinkage in regression benefit from these maximum likelihood insights.

The review consolidates key results from four ridge regression publications since 1975.

Abstract

My first paper exclusively about ridge regression was published in Technometrics and chosen for invited presentation at the 1975 Joint Statistical Meetings in Atlanta. Unfortunately, that paper contained a wide range of assorted details and results. Luckily, Gary McDonald's published discussion of that paper focused primarily on my use of Maximum Likelihood estimation under normal distribution-theory. In this review of some results from all four of my ridge publications between 1975 and 2022, I highlight the Maximum Likelihood findings that appear to be most important in practical application of shrinkage in regression.