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arXiv · 1403.1913

Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error density

Han Lin Shang
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Abstract

We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013, Computational Statistics & Data Analysis), we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya-Watson estimator that admits mixed types of regressors. We derive a kernel likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a nonparametric functional regression model with mixed types of regressors.

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Han Lin Shang. 2014-03-08. Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error density. https://doi.org/10.1080/10485252.2014.916806

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