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

Author

Listed:
  • Xibin Zhang

    (Department of Econometrics and Business Statistics, Monash Business School, Monash University, 900 Dandenong Road, Caulfield East, VIC 3145, Australia)

  • Maxwell L. King

    (Department of Econometrics and Business Statistics, Monash Business School, Monash University, 900 Dandenong Road, Caulfield East, VIC 3145, Australia)

  • Han Lin Shang

    (Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT 2601, Australia)

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.

Suggested Citation

  • Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:2:p:24-:d:68757
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    References listed on IDEAS

    as
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    Cited by:

    1. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    2. Xu, Bin & Lin, Boqiang, 2017. "Assessing CO2 emissions in China's iron and steel industry: A nonparametric additive regression approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 72(C), pages 325-337.

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    More about this item

    Keywords

    cross-validation; Nadaraya-Watson estimator; posterior predictive density; random-walk Metropolis; unknown error density; value-at-risk;
    All these keywords.

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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