Bayesian Adaptive Bandwidth Kernel Density Estimation of Irregular Multivariate Distributions
| Autor: | Xibin Zhang, Shuowen Hu, Donald Poskitt |
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| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Applied Mathematics Monte Carlo method Kernel density estimation Estimator Markov chain Monte Carlo jel:C11 jel:C14 Multivariate kernel density estimation jel:C15 Computational Mathematics symbols.namesake Minimum-variance unbiased estimator Computational Theory and Mathematics Econometric and statistical methods Variable kernel density estimation Statistics symbols conditional density global bandwidth Kullback-Leibler information marginal likelihood S&P500 index Econometrics not elsewhere classified Algorithm Invariant estimator Mathematics |
| DOI: | 10.26180/21433491.v1 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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