A useful semiparametric regression for climatology

Abstract

In climatology, there are several situations for which the response variable has linear and non-linear relations simultaneously in terms of explanatory variables. Another common situation in this area is when the distribution of the response variable presents a bimodal form. So, it is not possible analyzing this type of data using classical distributions belonging to the symmetric class (normal, t-Student, exponential power, etc.), or distributions in an asymmetric class (Weibull, log-logistic, skew normal, etc.). For these problems, we propose a semiparametric regression using a flexible distribution, named the odd log-logistic exponential Gaussian, whose systematic component contains parametric and nonparametric parts to measure the linear and non-linear effects simultaneously from a penalized smoothing based on the P-spline. We add new structural properties of the proposed distribution. Adopting penalized maximum likelihood to estimate the parameters and some simulations show the accuracy of the estimators. Diagnostic measures and residual analysis are discussed. We prove the versatility of our proposal in the climatology area.