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.
Citation
Priscila G. Silva. Audrey H. M. A. Cysneiros. Gauss M. Cordeiro. "Bias correction in power series generalized nonlinear models." Braz. J. Probab. Stat. 31 (3) 542 - 560, August 2017. https://doi.org/10.1214/16-BJPS323
Information