IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v78y2014icp218-234.html
   My bibliography  Save this article

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

Author

Listed:
  • Zhang, Xibin
  • King, Maxwell L.
  • Shang, Han Lin

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:218-234
    DOI: 10.1016/j.csda.2014.04.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314001376
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.04.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
    2. Linton, Oliver & Xiao, Zhijie, 2007. "A Nonparametric Regression Estimator That Adapts To Error Distribution Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(3), pages 371-413, June.
    3. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
    4. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    5. Max de Lima & Gregorio Atuncar, 2011. "A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 137-148.
    6. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    7. Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    9. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    10. 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.
    11. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    12. Tse, Y.K. & Zhang, Bill & Yu, Jun, 2002. "Estimation of Hyperbolic Diffusion using MCMC Method," Working Papers 182, Department of Economics, The University of Auckland.
    13. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    14. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    15. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    3. Guohua Feng & Chuan Wang & Xibin Zhang, 2019. "Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 1-19, February.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Guohua Feng & Chuan Wang & Xibin Zhang, 2019. "Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 1-19, February.
    7. 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.
    8. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    9. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    10. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    11. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    12. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
    13. Tsionas, Mike G. & Philippas, Dionisis & Philippas, Nikolaos, 2022. "Multivariate stochastic volatility for herding detection: Evidence from the energy sector," Energy Economics, Elsevier, vol. 109(C).
    14. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.
    15. Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    16. Nakajima, Jouchi & Kasuya, Munehisa & Watanabe, Toshiaki, 2011. "Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 225-245, September.
    17. Oskar Gustafsson & Mattias Villani & Pär Stockhammar, 2023. "Bayesian optimization of hyperparameters from noisy marginal likelihood estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 577-595, June.
    18. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    19. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    20. Xibin Zhang & Maxwell L. King & Rob J. Hyndman, 2004. "Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC," Monash Econometrics and Business Statistics Working Papers 9/04, Monash University, Department of Econometrics and Business Statistics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:218-234. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.