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

Xibin Zhang (), Maxwell King and Han Lin Shang

Computational Statistics & Data Analysis, 2014, vol. 78, issue C, 218-234

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.

Keywords: Bayes factors; Kernel-form error density; Metropolis–Hastings algorithm; Posterior predictive density; State-price density; Value-at-risk (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Working Paper: A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:78:y:2014:i:c:p:218-234

DOI: 10.1016/j.csda.2014.04.016

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