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Semiparametric Localized Bandwidth Selection in Kernel Density Estimation

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  • Tingting Cheng
  • Jiti Gao
  • Xibin Zhang

Abstract

Since conventional cross-validation bandwidth selection methods do not work for the case where the data considered are serially dependent, alternative bandwidth selection methods are needed. In recent years, Bayesian based global bandwidth selection methods have been proposed. Our experience shows that the use of a global bandwidth is however less suitable than using a localized bandwidth in kernel density estimation in the case where the data are serially dependent. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. In this paper, we propose a semiparametric estimation method and establish an asymptotic theory for the proposed estimator. A by-product of this bandwidth estimate is a new sampling-based likelihood approach to hyperparameter estimation. Monte Carlo simulation studies show that the proposed hyperparameter estimation method works very well, and that the proposed bandwidth estimator outperforms its competitors. Applications of the new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate, as well as the S&P 500 daily return under conditional heteroscedasticity, demonstrate the effectiveness and competitiveness of the proposed semiparametric localized bandwidth.

Suggested Citation

  • Tingting Cheng & Jiti Gao & Xibin Zhang, 2014. "Semiparametric Localized Bandwidth Selection in Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 14/14, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2014-14
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp14-14.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    4. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    5. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    6. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
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    Citations

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    Cited by:

    1. Sreevani, & Murthy, C.A., 2016. "On bandwidth selection using minimal spanning tree for kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 67-84.
    2. Tingting Cheng & Jiti Gao & Oliver Linton, 2017. "Multi-step non- and semi-parametric predictive regressions for short and long horizon stock return prediction," Monash Econometrics and Business Statistics Working Papers 13/17, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    hyperparameter estimation; likelihood score; localized bandwidth.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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