A Numerical Method to Obtain Exact Confidence Intervals for Likelihood-Based Parameter Estimators

Abstract

This study compares three distinct approaches for determining confidence intervals—the Bootstrap Method, Monte Carlo Simulation, and Wald Confidence Interval—within the framework of likelihood-based parameter estimation. Extensive simulations and practical evaluations spanning a wide range of statistical models are used to thoroughly analyze each approach's strengths and limitations in obtaining confidence intervals for various parameter estimators. This research exposes the nuanced strengths, shortcomings, and practical appropriateness of these approaches by thorough examination, considering their performance across varying sample sizes, model complexity, and data distributions. The findings provide useful recommendations for academics and practitioners by providing light on the best confidence interval estimate approach for likelihood-based parameter estimation in real-world statistical settings.