On the Robustness and Asymptotic Properties for Maximum Likelihood Estimators of Parameters in Exponential Power and its Scale Mixture Form Distributions

TL;DR

This paper investigates the robustness and asymptotic properties of maximum likelihood estimators for parameters in exponential power and scale mixture distributions, providing theoretical insights and iterative algorithms for estimation.

Contribution

It offers a comprehensive analysis of the robustness measures and asymptotic behavior of ML estimators in these distributions, including iterative reweighting algorithms for parameter estimation.

Findings

Asymptotic properties of ML estimators are established.

Robustness measures such as influence function and breakdown point are analyzed.

Iterative algorithms for simultaneous estimation of parameters are developed.

Abstract

The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to overcome the problem for modelling non-normal data set since last decades. However, examining the robustness properties of maximum likelihood (ML) estimators of parameters in these distributions, such as the in uence function, gross-error sensitivity, breakdown point and information-standardized sensitivity, has not been considered together. The well-known asymptotic properties of ML estimators of location, scale and added skewness parameters in EP and its scale mixture form distributions are studied and also these ML estimators for location, scale and scale variant (skewness) parameters can be represented as an iterative reweighting algorithm to compute the estimates of these parameters simultaneously.