A Bayesian approach to parameter estimation for kernel density estimation via transformations

Qing Liu, David Pitt, Xibin Zhang, Xueyuan Wu

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.
Original languageEnglish
Pages (from-to)181 - 193
Number of pages13
JournalAnnals of Actuarial Science
Volume5
Issue number2
DOIs
Publication statusPublished - 2011

Cite this

@article{099ed55402d140dc8859cd846866ab9f,
title = "A Bayesian approach to parameter estimation for kernel density estimation via transformations",
abstract = "In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.",
author = "Qing Liu and David Pitt and Xibin Zhang and Xueyuan Wu",
year = "2011",
doi = "10.1017/S1748499511000030",
language = "English",
volume = "5",
pages = "181 -- 193",
journal = "Annals of Actuarial Science",
issn = "1748-4995",
publisher = "Cambridge University Press",
number = "2",

}

A Bayesian approach to parameter estimation for kernel density estimation via transformations. / Liu, Qing; Pitt, David; Zhang, Xibin; Wu, Xueyuan.

In: Annals of Actuarial Science, Vol. 5, No. 2, 2011, p. 181 - 193.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A Bayesian approach to parameter estimation for kernel density estimation via transformations

AU - Liu, Qing

AU - Pitt, David

AU - Zhang, Xibin

AU - Wu, Xueyuan

PY - 2011

Y1 - 2011

N2 - In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

AB - In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

U2 - 10.1017/S1748499511000030

DO - 10.1017/S1748499511000030

M3 - Article

VL - 5

SP - 181

EP - 193

JO - Annals of Actuarial Science

JF - Annals of Actuarial Science

SN - 1748-4995

IS - 2

ER -