A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density

Xibin Zhang*, Maxwell L. King, Han Lin Shang

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The unknown error density of a nonparametric regression model is approximated by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. Such a mixture density has the form of a kernel density estimator of error realizations. An approximate likelihood and posterior for bandwidth parameters in the kernel-form error density and the Nadaraya–Watson regression estimator are derived, and a sampling algorithm is developed. A simulation study shows that when the true error density is non-Gaussian, the kernel-form error density is often favored against its parametric counterparts including the correct error density assumption. The proposed approach is demonstrated through a nonparametric regression model of the Australian All Ordinaries daily return on the overnight FTSE and S&P 500 returns. With the estimated bandwidths, the one-day-ahead posterior predictive density of the All Ordinaries return is derived, and a distribution-free value-at-risk is obtained. The proposed algorithm is also applied to a nonparametric regression model involved in state-price density estimation based on S&P 500 options data.
Original languageEnglish
Pages (from-to)218-234
Number of pages17
JournalComputational Statistics and Data Analysis
Volume78
DOIs
Publication statusPublished - Oct 2014
Externally publishedYes

Keywords

  • Bayes factors
  • Kernel-form error density
  • Metropolis–Hastings algorithm
  • Posterior predictive density
  • State-price density
  • Value-at-risk
  • Metropolis-Hastings algorithm

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