## Brazilian Journal of Probability and Statistics

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

### Bias correction in power series generalized nonlinear models

Priscila G. Silva, Audrey H. M. A. Cysneiros, and Gauss M. Cordeiro

#### 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**

Received: August 2015

Accepted: June 2016

First available in Project Euclid: 22 August 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/16-BJPS323

**Mathematical Reviews number (MathSciNet)**

MR3693980

**Zentralblatt MATH identifier**

1377.62158

**Keywords**

Bias correction discrete distribution maximum likelihood scoring method nonlinear model

#### 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