Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

Research output: Contribution to journalArticle

Abstract

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.
Original languageEnglish
Number of pages22
JournalJournal of Applied Statistics
DOIs
Publication statusE-pub ahead of print - 3 Mar 2020

Keywords

  • Functional Nadaraya-Watson estimator
  • Gaussian kernel mixture
  • Markov chain Monte Carlo
  • error-density estimation
  • scalar-on-function regression
  • spectroscopy

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