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