Birnbaum-Saunders Semi-Parametric Additive Modeling: Estimation, Smoothing, Diagnostics, And Application

Inclusion of nonparametric functions enhances the modeling when accommodating non-linear effects of covariates. Semi-parametric models have been successfully used for describing non-linear structures by means of parametric and nonparametric components. In this work, we formulate a semi-parametric additive regression model based on a Birnbaum–Saunders distribution and carry out influence diagnostics for such a model. This semi-parametric structure permits us to model the mean and variance simultaneously. We employ a back-fitting algorithm to get the penalized maximum likelihood estimates by utilizing cubic smoothing splines. We derive methods of local influence by calculating the normal curvatures under different perturbation schemes. The obtained results are computationally implemented in the R software so that diverse users have available this model computationally to be applied in practice. Finally, an application of the proposed model with real data from one of the most polluted cities in the world is presented.