Bayesian bandwidth selection for a nonparametric regression model with mixed types of regressors

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Abstract

This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the unobserved errors, while the regression function is estimated using the Nadaraya-Watson estimator admitting continuous and discrete regressors. We derive an approximate likelihood and posterior for bandwidth parameters, followed by a sampling algorithm. Simulation results show that the proposed approach typically leads to better accuracy of the resulting estimates than cross-validation, particularly for smaller sample sizes. This bandwidth estimation approach is applied to nonparametric regression model of the Australian All Ordinaries returns and the kernel density estimation of gross domestic product (GDP) growth rates among the organisation for economic co-operation and development (OECD) and non-OECD countries.
Original languageEnglish
Article number24
Number of pages27
JournalEconometrics
Volume4
Issue number2
DOIs
Publication statusPublished - 2016

Keywords

  • cross-validation
  • Nadaraya-Watson estimator
  • posterior predictive density
  • random-walk Metropolis
  • unknown error density
  • value-at-risk

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