Asymptotic adjustments of Pearson residuals in exponential family nonlinear models. Issue 8 (24th May 2017)

• Record Type: Journal Article
• Authors: Rocha, Andréa V.; Simas, Alexandre B.
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 8(2017)
• Page Start: 1684
• Page End: 1700
• Publication Date: 2017-05-24
• Subjects: Exponential family -- nonlinear models -- Pearson residuals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1281926
• Languages: English
• ISSNs: 0094-9655

Abstract

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 orderO ( n − 1 ), 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].