Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density. Issue 4 (12th March 2021)

• Record Type: Journal Article
• Authors: Shang, Han Lin
• Is Part Of: Journal of applied statistics. Volume 48:Issue 4(2021)
• Page Start: 583
• Page End: 604
• Publication Date: 2021-03-12
• Subjects: Functional Nadaraya-Watson estimator -- scalar-on-function regression -- Gaussian kernel mixture -- Markov chain Monte Carlo -- error-density estimation -- spectroscopy; 97K80 -- 62F15; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2020.1736527
• Languages: English
• ISSNs: 0266-4763

Abstract

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.