Bayesian Bandwidth Estimation for a Semi-Functional Partial Linear Regression Model with Unknown Error Density

• Activity Number: 188
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Han Lin Shang*+
• Companies: University of Southampton
• Keywords: functional Nadaraya-Watson estimator ; functional regression ; Gaussian kernel mixture ; error density estimation ; Markov chain Monte Carlo

Abstract

In semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya-Watson estimators. The estimation accuracy of regression function depends on a common bandwidth parameter. We propose a Bayesian procedure to simultaneously estimate the bandwidths in the kernel-form error density and regression function. We derive a kernel likelihood and posterior for the bandwidth parameters. A series of simulation studies show that the Bayesian procedure yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that not only the Bayesian procedure gives better point forecast accuracy of the regression function than the functional cross validation, but it is also capable of producing prediction intervals nonparametrically.