Asymptotic adjustments of Pearson residuals in exponential family nonlinear models

ABSTRACT

In this work we define a set of corrected Pearson residuals for continuous exponential family nonlinear models that have the same distribution as the true Pearson residuals up to order $\mathcal{O}\left(n^{-1}\right)$, where n is the sample size. Furthermore, we also introduce a new modification of the Pearson residuals, which we call PCA Pearson residuals, that are approximately uncorrelated. These PCA residuals are new even for the generalized linear models. The numerical results show that the PCA residuals are approximately normally distributed, thus improving previous results by Simas and Cordeiro [Adjusted Pearson residuals in exponential family nonlinear models. J Stat Comput Simul. 2009;79:411–425]. These numerical results also show that the corrected Pearson residuals approximately follow the same distribution as the true residuals, which is a considerable improvement with respect to the Pearson residuals and also extends the previous work by Cordeiro and Simas [The distribution of Pearson residuals in generalized linear models. Comput Stat Data Anal. 2009;53:3397–3411].

KEYWORDS:

• Exponential family
• nonlinear models
• Pearson residuals

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by CNPq (Conselho Nacional de Desenvolvimento Cientìfico e Tecnológico) under grant no. 309097/2012-6,309947/2015-4.