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Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions

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  • Hu, Shuowen
  • Poskitt, D.S.
  • Zhang, Xibin

Abstract

In this paper, we propose a new methodology for multivariate kernel density estimation in which data are categorized into low- and high-density regions as an underlying mechanism for assigning adaptive bandwidths. We derive the posterior density of the bandwidth parameters via the Kullback–Leibler divergence criterion and use a Markov chain Monte Carlo (MCMC) sampling algorithm to estimate the adaptive bandwidths. The resulting estimator is referred to as the tail-adaptive density estimator. Monte Carlo simulation results show that the tail-adaptive density estimator outperforms the global-bandwidth density estimators implemented using different global bandwidth selection rules. The inferential potential of the tail-adaptive density estimator is demonstrated by employing the estimator to estimate the bivariate density of daily index returns observed from the USA and Australian stock markets.

Suggested Citation

  • Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:732-740 DOI: 10.1016/j.csda.2011.09.022
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    Cited by:

    1. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, pages 732-740.
    2. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    3. 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.

    More about this item

    Keywords

    Marginal likelihood; Markov chain Monte Carlo; S&P 500 index; Value-at-risk;

    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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