Analyzing the Role of Empirical Process Theory in Developing Modern Statistical Estimation Techniques

Posted: Feb 28, 2019

• Brooke Stewart
• Caleb Ross
• Cameron Murphy

Abstract

The landscape of statistical estimation has undergone significant transformation in recent decades, driven by the increasing complexity of data structures and the demand for methods that remain valid under minimal assumptions. Empirical process theory, once considered an esoteric branch of theoretical probability, has emerged as a fundamental tool for developing modern statistical estimation techniques that address these challenges. This paper examines the profound impact of empirical process theory on the design, analysis, and implementation of statistical estimators, with particular emphasis on nonparametric and high-dimensional settings where traditional asymptotic theory often fails to provide adequate guidance.