On the Weak Convergence and Central Limit Theorem of Blurring and Nonblurring Processes with Application to Robust Location Estimation

TL;DR

This paper investigates the weak convergence and CLT of blurring and nonblurring processes, demonstrating their application to robust location estimation with simulations showing improved robustness and efficiency of blurring-based methods.

Contribution

It provides new theoretical results on the convergence properties of blurring processes and applies these findings to develop more robust location estimators.

Findings

Blurring processes exhibit favorable convergence properties for robust estimation.

Location estimators based on blurring processes are more robust than nonblurring ones.

Simulation results confirm the efficiency and robustness of the proposed methods.

Abstract

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation based on the convergence point of blurring process is more robust and often more efficient than that of nonblurring process.