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Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions

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

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.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 3 ()
Pages: 732-740

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Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:732-740
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