Modelos Lineares Generalizados Semiparamétricos

Abstract

In this research, the Generalized Linear Model (GLM) was extended to the Generalized Semiparametric Linear Model by adding a non-parametric curve to the MLG systematic component. The Binomial, Gamma, Gaussian Inverse, Normal and Poisson distributions and their main links were considered for the study. The nodes of the non-parametric curve were constructed using the methods of Eilers and Marks (1996) and Green and Silverman (1994). The selection of the smoothing parameter was made by Cross Validation. The methods for estimating the parameters and the non-parametric curve were developed using Newton's Scoring iterative method, as well as the calculations of the Fisher information matrix and the score function. Lastly, with the aid of the statistical software R (R Core Team, 2021), the estimation codes were elaborated and simulation studies were carried out to evaluate the efficiency of the parameter estimation method, in addition to the application in pollen data from Kalamazoo Ambrosia in 1993.