Maximum Lq-Likelihood Estimation for Gamma Distributions
Date
2015-06-19
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Abstract
MLqE is an extension of MLE which introduces a distortion parameter q to MLE to make the estimation more adaptive. The purpose of this thesis is to examine MLqE for specific distribution models. Particularly, for exponential and standard gamma distributions, we look at their asymptotics, finite sample performance in terms of efficiency and robustness, and the choice of the distortion parameter q. We investigate these aspects of MLqE, compared with MLE, in parameter estimation and tail probability estimation through both Monte Carlo simulation and a real data analysis. Our results show that, when exponential or standard gamma models are concerned, MLqE and MLE perform competitively for large sample sizes while MLqE outperforms MLE for small or moderate sample size in terms of reducing MSE. In addition, MLqE generally has better robustness properties than MLE with respect to outlying observations.
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Citation
Xing, N. (2015). Maximum Lq-Likelihood Estimation for Gamma Distributions (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26841