Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions
Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions
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DOI：
10.1016/j.csda.2011.09.022
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发表时间：
2012-03
期刊：
影响因子：
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通讯作者：
Shuowen Hu;D. Poskitt;Xibin Zhang
中科院分区：
文献类型：
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作者：
Shuowen Hu;D. Poskitt;Xibin Zhang
在本文中，我们提出了一种新的多元核密度估计方法，其中将数据分为低密度和高密度区域，作为分配自适应带宽的基本机制。我们通过Kullback-Leibler散度准则推导出带宽参数的后验密度，并使用马尔可夫链蒙特卡罗（MCMC）采样算法估计自适应带宽。得到的估计量称为尾自适应密度估计量。蒙特卡罗仿真结果表明，尾部自适应密度估计器优于采用不同全局带宽选择规则实现的全局带宽密度估计器。利用尾自适应密度估计器估计美国和澳大利亚股票市场观察到的每日指数回报的二元密度，证明了尾自适应密度估计器的推断潜力。
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.