Bayesian Adaptive Bandwidth Kernel Density Estimation of Irregular Multivariate Distributions

Shuowen Hu (), Donald Poskitt and Xibin Zhang ()

No 21/10, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Kernel density estimation is an important technique for understanding the distributional properties of data. Some investigations have found that the estimation of a global bandwidth can be heavily affected by observations in the tail. We propose to categorize data into low- and high-density regions, to which we assign two different bandwidths called the low-density adaptive bandwidths. We derive the posterior of the bandwidth parameters through the Kullback-Leibler information. A Bayesian sampling algorithm is presented to estimate the bandwidths. Monte Carlo simulations are conducted to examine the performance of the proposed Bayesian sampling algorithm in comparison with the performance of the normal reference rule and a Bayesian sampling algorithm for estimating a global bandwidth. According to Kullback-Leibler information, the kernel density estimator with low-density adaptive bandwidths estimated through the proposed Bayesian sampling algorithm outperforms the density estimators with bandwidth estimated through the two competitors. We apply the low-density adaptive kernel density estimator to the estimation of the bivariate density of daily stock-index returns observed from the U.S. and Australian stock markets. The derived conditional distribution of the Australian stock-index return for a given daily return in the U.S. market enables market analysts to understand how the former market is associated with the latter.

Keywords: conditional density; global bandwidth; Kullback-Leibler information; marginal likelihood; Markov chain Monte Carlo; S&P500 index (search for similar items in EconPapers)
JEL-codes: C11 C14 C15 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2010-12
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions (2012)
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