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February 2018 Improved estimation in a general multivariate elliptical model
Tatiane F. N. Melo, Silvia L. P. Ferrari, Alexandre G. Patriota
Braz. J. Probab. Stat. 32(1): 44-68 (February 2018). DOI: 10.1214/16-BJPS331


The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in common. Many frequently used models are special cases of this general formulation, namely: errors-in-variables models, nonlinear mixed-effects models, heteroscedastic nonlinear models, among others. In any of these models, the vector of the errors may have any multivariate elliptical distribution. We obtain the second-order bias of the maximum likelihood estimator, a bias-corrected estimator, and a bias-reduced estimator. Simulation results indicate the effectiveness of the bias correction and bias reduction schemes.


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Tatiane F. N. Melo. Silvia L. P. Ferrari. Alexandre G. Patriota. "Improved estimation in a general multivariate elliptical model." Braz. J. Probab. Stat. 32 (1) 44 - 68, February 2018.


Received: 1 January 2016; Accepted: 1 July 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06973948
MathSciNet: MR3770863
Digital Object Identifier: 10.1214/16-BJPS331

Keywords: bias correction , bias reduction , elliptical model , general parameterization , maximum likelihood estimation

Rights: Copyright © 2018 Brazilian Statistical Association


Vol.32 • No. 1 • February 2018
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