## Brazilian Journal of Probability and Statistics

### Bias correction in power series generalized nonlinear models

#### Abstract

Power series generalized nonlinear models [Comput. Statist. Data Anal. 53 (2009) 1155–1166] can be used when the Poisson assumption of equidispersion is not valid. In these models, we consider a more general family of discrete distributions for the response variable and a nonlinear structure for the regression parameters, although the dispersion parameter and other shape parameters are assumed known. We derive a general matrix formula for the second-order bias of the maximum likelihood estimate of the regression parameter vector in these models. We use the results by [J. Roy. Statist. Soc. B 30 (1968) 248–275] and bootstrap technique [Ann. Statist. 7 (1979) 1–26] to obtain the bias-corrected maximum likelihood estimate. Simulation studies are performed using different estimates. We also present an empirical application.

#### Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 3 (2017), 542-560.

Dates
Accepted: June 2016
First available in Project Euclid: 22 August 2017

https://projecteuclid.org/euclid.bjps/1503388828

Digital Object Identifier
doi:10.1214/16-BJPS323

Mathematical Reviews number (MathSciNet)
MR3693980

Zentralblatt MATH identifier
1377.62158

#### Citation

Silva, Priscila G.; Cysneiros, Audrey H. M. A.; Cordeiro, Gauss M. Bias correction in power series generalized nonlinear models. Braz. J. Probab. Stat. 31 (2017), no. 3, 542--560. doi:10.1214/16-BJPS323. https://projecteuclid.org/euclid.bjps/1503388828

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