Robust Strongly Convergent M-Estimators Under Non-IID Assumption

TL;DR

This paper investigates the strong convergence properties of M-estimators in generalized linear models under minimal assumptions, extending results to non-i.i.d. data and illustrating implications for binary and continuous models.

Contribution

It provides a novel analysis of M-estimators' convergence under non-i.i.d. conditions, broadening the theoretical understanding beyond traditional i.i.d. frameworks.

Findings

Established strong convergence of M-estimators in non-i.i.d. settings

Derived an expansion of estimating operators applicable to various models

Discussed implications for binary and continuous response models

Abstract

M-estimators for Generalized Linear Models are considered under minimal assumptions. Under these preliminaries, strong convergence of the estimators are discussed and an expansion of the estimating operators are given in the non-i.i.d. case with the i.i.d. case shown as a particular application. Various consequences of the results are discussed for binary and continuous models.