Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

Han Lin Shang*

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In the context of 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 the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically.
Original languageEnglish
Pages (from-to)829–848
Number of pages20
JournalComputational Statistics
Volume29
Issue number3-4
DOIs
Publication statusPublished - Jun 2014
Externally publishedYes

Keywords

  • Functional Nadaraya–Watson estimator
  • Functional regression
  • Gaussian kernel mixture
  • Error density estimation
  • Markov chain Monte Carlo
  • Functional Nadaraya-Watson estimator

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