Estimation of a functional single index model with dependent errors and unknown error density. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Shang, Han Lin
• Is Part Of: Communications in statistics. Volume 49:Issue 12(2020)
• Page Start: 3111
• Page End: 3133
• Publication Date: 2020-12-01
• Subjects: Error density estimation -- Gaussian kernel mixture -- Markov chain Monte Carlo -- Nadaraya-Watson estimator -- Scalar-on-function regression -- Spectroscopy; 62G07 -- 62G08 -- 62G09; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1535068
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function, under an autoregressive error structure. For estimating both the regression function and error density, empirical studies show that the functional single index model gives improved estimation and prediction accuracies than any nonparametric functional regression considered. Furthermore, estimation of error density facilitates the construction of prediction interval for the response variable.