Maximum Likelihood Estimation and Likelihood Ratio Test Revisited

Vinaitheerthan Renganathan

Abstract

Maximum likelihood Estimation is an important aspect of the frequentist approach which was introduced by R.A. Fisher. The Maximum Likelihood estimation method helps us to find the estimator for the unknown population parameter. There are other methods of estimation also available such as Least Square Estimation and Bayesian Estimation methods, but Maximum Likelihood Estimation is the widely used method to estimate parameters. This paper provides an overview of the Maximum Likelihood Method with an example to calculate a Maximum Likelihood Estimator from a sample data set.

Keywords: Maximum Likelihood, Frequentist

Introduction

Maximum Likelihood estimation (MLE) is a widely used statistical approach to find parameter estimators for a variety of statistical models. Maximum likelihood estimation methods are being used to estimate parameters in generalized linear models such as logistic regression models, probit models, mixed models, and survival analysis models. The primary objective of the Maximum Likelihood Estimation is to select values of the unknown parameter that maximize the likelihood of obtaining the observed sample data points under study.