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

Research output: Contribution to journalArticleResearchpeer-review

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

Cite this

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title = "Bayesian bandwidth selection for a nonparametric regression model with mixed types of regressors",
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.",
keywords = "cross-validation, Nadaraya-Watson estimator, posterior predictive density, random-walk Metropolis, unknown error density, value-at-risk",
author = "Xibin Zhang and King, {Maxwell L.} and Shang, {Han Lin}",
year = "2016",
doi = "10.3390/econometrics4020024",
language = "English",
volume = "4",
journal = "Econometrics",
issn = "2225-1146",
publisher = "MDPI",
number = "2",

}

Bayesian bandwidth selection for a nonparametric regression model with mixed types of regressors. / Zhang, Xibin; King, Maxwell L.; Shang, Han Lin .

In: Econometrics, Vol. 4, No. 2, 24, 2016.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Bayesian bandwidth selection for a nonparametric regression model with mixed types of regressors

AU - Zhang, Xibin

AU - King, Maxwell L.

AU - Shang, Han Lin

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - cross-validation

KW - Nadaraya-Watson estimator

KW - posterior predictive density

KW - random-walk Metropolis

KW - unknown error density

KW - value-at-risk

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DO - 10.3390/econometrics4020024

M3 - Article

VL - 4

JO - Econometrics

JF - Econometrics

SN - 2225-1146

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