Application of Random Matrix Theory in High-Dimensional Statistics

TL;DR

This review explores how random matrix theory enhances high-dimensional statistical methods, addressing challenges in covariance inference, PCA, and signal processing through key theoretical insights and practical applications.

Contribution

It provides a comprehensive overview of RMT's impact on high-dimensional statistics, highlighting recent theoretical advances and their practical implications.

Findings

RMT offers powerful tools for covariance matrix inference.

Advances in RMT improve PCA and changepoint detection methods.

Theoretical results from RMT have been successfully applied in practice.

Abstract

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics, we explore key theoretical results from RMT and their role in addressing challenges associated with high-dimensional data. The discussion highlights how advances in RMT have significantly influenced the development of statistical methods, particularly in areas such as covariance matrix inference, principal component analysis (PCA), signal processing, and changepoint detection, demonstrating the close interplay between theory and practice in modern high-dimensional statistical inference.