# Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error density

arXiv: https://arxiv.org/abs/1403.1913 · HTML: https://mlsanity.com/paper/1403.1913/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2014.

## Built on by (most cited first, 1 of 1)

- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)

## Abstract (arXiv)

We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013, Computational Statistics & Data Analysis), we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya-Watson estimator that admits mixed types of regressors. We derive a kernel likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a nonparametric functional regression model with mixed types of regressors.