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

TL;DR

This paper introduces a Bayesian approach for estimating a functional single index model with dependent errors, improving estimation accuracy and enabling prediction intervals by jointly estimating the regression function and error density.

Contribution

It develops a novel Bayesian method for simultaneous estimation of the regression function and error density in a dependent error setting, enhancing prediction and inference.

Findings

Bayesian method effectively estimates regression and error density.

Improved prediction accuracy over nonparametric models.

Error density estimation enables construction of prediction intervals.

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.