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Open AccessArticle

Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors

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Department of Econometrics and Business Statistics, Monash Business School, Monash University, 900 Dandenong Road, Caulfield East, VIC 3145, Australia
2
Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT 2601, Australia
*
Author to whom correspondence should be addressed.
Academic Editor: Isabel Casas
Econometrics 2016, 4(2), 24; https://doi.org/10.3390/econometrics4020024
Received: 8 December 2015 / Revised: 5 April 2016 / Accepted: 6 April 2016 / Published: 22 April 2016
(This article belongs to the Special Issue Nonparametric Methods in Econometrics)
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. View Full-Text
Keywords: cross-validation; Nadaraya-Watson estimator; posterior predictive density; random-walk Metropolis; unknown error density; value-at-risk cross-validation; Nadaraya-Watson estimator; posterior predictive density; random-walk Metropolis; unknown error density; value-at-risk
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Zhang, X.; King, M.L.; Shang, H.L. Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors. Econometrics 2016, 4, 24.

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