A. Coín, J. R. Berrendero, A. Cuevas
In this communication we propose a Bayesian approach for functional linear or logistic regression models, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS’s). These new models build upon the RKHS associated with the covariance function of the underlying stochastic process, and can be viewed as finite-dimensional alternatives to classical functional regression models.
The corresponding functional model (or the functional logistic equation in the case of binary response) is determined by a function living on a dense subset of the RKHS generated by the underlying covariance function. By imposing a suitable prior distribution on such RKHS, we can perform data-driven inference via standard Bayes methodology. The posterior distribution can be approximated from Markov Chain Monte Carlo (MCMC) methods. Several estimators derived from this posterior distribution turn out to be competitive against other usual alternatives in both simulated examples and real datasets.
Keywords: Functional data, linear regression, logistic regression, reproducing kernel Hilbert spaces, Bayesian methods
Scheduled
GT06 Functional Data Analysis III. Recent contributions
June 8, 2022 5:20 PM
Grade Hall
