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A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

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  • Zhang, Xibin
  • Brooks, Robert D.
  • King, Maxwell L.

Abstract

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow-Debreu securities with the S&P 500 index options data and the DAX index options data. The proposed Bayesian bandwidth selector represents a data-driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state-price density pioneered by Aït-Sahalia and Lo [Aït-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. The Journal of Finance, 53, 499, 547.]

Suggested Citation

  • Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
  • Handle: RePEc:eee:econom:v:153:y:2009:i:1:p:21-32
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    Cited by:

    1. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0709-3 is not listed on IDEAS
    2. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-27, April.
    3. Zhang, Xibin & King, Maxwell L. & Shang, Han Lin, 2014. "A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 218-234.
    4. Anastasios Panagiotelis & Michael S. Smith & Peter J. Danaher, 2014. "From Amazon to Apple: Modeling Online Retail Sales, Purchase Incidence, and Visit Behavior," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 14-29, January.
    5. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.
    6. Tristan Senga Kiessé & Nabil Zougab & Célestin C. Kokonendji, 2016. "Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data," Computational Statistics, Springer, vol. 31(1), pages 189-206, March.
    7. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    8. Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
    9. Oliver Morell & Dennis Otto & Roland Fried, 2013. "On robust cross-validation for nonparametric smoothing," Computational Statistics, Springer, vol. 28(4), pages 1617-1637, August.
    10. Rong Zhang & Brett A. Inder & Xibin Zhang, 2012. "Parameter estimation for a discrete-response model with double rules of sample selection: A Bayesian approach," Monash Econometrics and Business Statistics Working Papers 5/12, Monash University, Department of Econometrics and Business Statistics.
    11. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    12. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    13. repec:gam:jecnmx:v:4:y:2016:i:2:p:24:d:68757 is not listed on IDEAS
    14. Feng, Guohua & Zhang, Xiaohui, 2014. "Returns to scale at large banks in the US: A random coefficient stochastic frontier approach," Journal of Banking & Finance, Elsevier, vol. 39(C), pages 135-145.
    15. Zhang, Rong & Inder, Brett A. & Zhang, Xibin, 2015. "Bayesian estimation of a discrete response model with double rules of sample selection," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 81-96.
    16. Hart, Jeffrey D. & Choi, Taeryon & Yi, Seongbaek, 2016. "Frequentist nonparametric goodness-of-fit tests via marginal likelihood ratios," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 120-132.
    17. Rong Zhang & Brett A. Inder & Xibin Zhang, 2013. "Bayesian estimation of a discrete response model with double rules of sample selection," Monash Econometrics and Business Statistics Working Papers 24/13, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Black-Scholes formula Bootstrapping Cross-validation Markov chain Monte Carlo Time to maturity;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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