Estimation of a functional single index model with dependent errors and unknown error density

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.

Keywords:

• Error density estimation
• Gaussian kernel mixture
• Markov chain Monte Carlo
• Nadaraya-Watson estimator
• Scalar-on-function regression
• Spectroscopy

MSC 2010:

• 62G07
• 62G08
• 62G09

Acknowledgments

The author thanks Dr. Juhyun Park for fruitful discussions, and acknowledges the hospitality of the Department of Statistics and Actuarial Science at the University of Waterloo while preparing the paper. This project was funded by a faculty research grant from the College of Business and Economics, Australian National University.