Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications

Autor: Yolanda M. Gómez, Bruno Santos, Diego I. Gallardo, Osvaldo Venegas, Héctor W. Gómez
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Revstat Statistical Journal, Vol 21, Iss 4 (2023)
Druh dokumentu: article
ISSN: 1645-6726
2183-0371
Popis: 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.
Databáze: Directory of Open Access Journals