A Partially Varying‐Coefficient Model With Skew‐T Random Errors for Environmental Data Modeling

Partially varying‐coefficient models (PVCMs) are an important tool in the modeling of environmental, economic, biomedical and other data, which have a parametric and a nonparametric component in their formulation. In addition to presenting interaction of the unknown smooth functions, which makes the classic linear regression models more flexible, such that generalizes to generalized additive models (GAMs) and models with varying coefficients (VCMs), which usually have a Gaussian distribution. In many cases the data tend to be more complex in the sense that they can present high levels of skewness and kurtosis. This article extends the version Gaussian PVCMs, allowing errors to present asymmetry and heavy tails, increasing the flexibility of this type of models where the Gaussian version remains a special case within this extended version. Specifically, the EM algorithm was developed for the estimation of parameters and development of diagnostic analysis through local influence. To evaluate the efficiency of the estimation, a simulation study was carried out. Finally, the model was applied to the datasets of the National Air Quality Information System (SINCA) of Chile, specifically to data of the Metropolitan Region of Santiago, considering as the study variable the particulate matter PM2.5$$ {\mathrm{PM}}_{2.5} $$, for the importance it represents in environmental pollution and population health issues.