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

Han Lin Shang*

*Corresponding author for this work

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We investigate the issue of bandwidth estimation in a functional nonparametric 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) [‘Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density’, Computational Statistics & Data Analysis, 67, 185–198], 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 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 functional nonparametric regression model with mixed types of regressors.
Original languageEnglish
Pages (from-to)599-615
Number of pages17
JournalJournal of Nonparametric Statistics
Volume26
Issue number3
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • functional Nadaraya–Watson estimator
  • kernel density estimation
  • Markov chain Monte Carlo
  • mixture error density
  • spectroscopy
  • functional Nadaraya-Watson estimator

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