Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error...

Area of Science:

• Statistics
• Functional Data Analysis

Background:

• Accurate estimation of regression functions and error densities is crucial in functional data analysis.
• Existing methods may not optimally select bandwidth and semi-metric parameters.

Purpose of the Study:

• To develop an optimal functional partial linear model.
• To improve estimation and forecast accuracy for functional data.
• To propose a Bayesian method for simultaneous bandwidth and semi-metric estimation.

Main Methods:

• Estimating error density using kernel density estimation.
• Employing functional principal component and Nadayara-Watson estimators for regression components.
• Utilizing a Bayesian approach to minimize Kullback-Leibler divergence for optimal parameter selection.

Main Results:

• The proposed functional partial linear model demonstrates superior estimation and forecast accuracy in simulations.
• The model outperforms functional principal component regression and functional nonparametric regression.
• The functional partial linear model shows better forecast accuracy on a spectroscopy dataset.

Conclusions:

• The Bayesian method effectively estimates bandwidth and semi-metric, enhancing functional regression models.
• The functional partial linear model offers improved predictive performance for functional data.
• Pointwise prediction intervals and semi-metric selection are facilitated by the Bayesian approach.