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

Han Lin Shang1,2

  • 1Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, Australia.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces an optimal functional partial linear model for improved estimation and forecasting. The Bayesian method enhances accuracy for bandwidth and semi-metric selection in functional data analysis.

Keywords:
62F1597K80Functional Nadaraya-Watson estimatorGaussian kernel mixtureMarkov chain Monte Carloerror-density estimationscalar-on-function regressionspectroscopy

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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.