Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications
Authors
Gomez, Yolanda M.
Santos, Bruno
Gallardo, Diego, I
Venegas, Osvaldo
Gomez, Hector W.
Santos, Bruno
Gallardo, Diego, I
Venegas, Osvaldo
Gomez, Hector W.
Profesor GuĆa
Authors
Date
Datos de publicaciĆ³n:
10.57805/revstat.v21i4.431
REVSTAT-STATISTICAL JOURNAL,Vol.21,491-507,2023
Tipo de recurso
WOS
Keywords
Materia geogrƔfica
Collections
Abstract
In this paper we study some methods to reduce the bias for maximum likelihood estimation in the general class of alpha power models, specifically for the shape parameter. We find the modified maximum likelihood estimator using Firth's method and we show that this estimator is the uniformly minimum variance unbiased estimator (UMVUE) in this class. We consider three special cases of this class, namely the exponentiated exponential (EE), the power half -normal and the power piecewise exponential models. We compare the bias in simulation studies and find that the modified method is definitely superior, especially for small sample sizes, in both the bias and the root mean squared error. We illustrate our modified estimator in four real data set examples, in each of which the modified estimates better explain the variability.