  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 $\mathcal{O}(n^{-1})$, 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
(2009). 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 (2009).
