Partially Linear Additive Models

Authors

Keywords:

Partially Linear Additive Models, B-Splines, Penalized Maximum Likelihood

Abstract

In the present work, partially linear additive models are presented. This means an extension of linear models that incorporate non-linear components to model more complex relationships between independent variables and the response variable. The goal of the work is to study these models and implement an algorithm that enables parameter estimation. B-Splines are used
to describe the non-parametric components. Considering the penalized likelihood function, we obtain maximum likelihood estimators as well as the Fisher information matrix, which is used to obtain standard error estimates for the parameter estimators. Additionally, the Bayesian information criterion is used for parameter smoothing selection. Simulation studies were conducted to verify the asymptotic properties of the maximum likelihood estimators. Finally, to illustrate the utility of the proposed model, it was applied to a dataset on mortality in the city of Milan, Italy. Non-linear explanatory variables include temperature and humidity, while linear variables include the number of suspended particles in the air and time (in days).

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Published

08-03-2024

How to Cite

Toledo , C., Lopes , J., & Ferreira , C. (2024). Partially Linear Additive Models. Sigmae, 13(1), 24–31. Retrieved from https://publicacoes.unifal-mg.edu.br/revistas/index.php/sigmae/article/view/2275