Transformation-based nonparametric estimation of multivariate densities

Meng-Shiuh Chang and Ximing Wu ()

Journal of Multivariate Analysis, 2015, vol. 135, issue C, 71-88

Abstract: We present a probability-integral-transformation-based estimator of multivariate densities. Given a sample of random vectors, we first transform the data into their corresponding marginal distributions. The marginal densities and the joint density of the transformed data are estimated nonparametrically. The joint density of the original data is constructed as the product of the density of the transformed data and marginal densities, which coincides with the copula representation of multivariate densities. We show that the Kullback–Leibler Information Criterion (KLIC) between the true density and its estimate can be decomposed into the KLIC of the marginal densities and that of the copula density. We derive the convergence rate of the proposed estimator in terms of the KLIC and propose a supervised hierarchical procedure of model selection. Monte Carlo simulations demonstrate the good performance of the estimator. An empirical example on the US and UK stock markets is presented. The estimated conditional copula density provides useful insight into the joint movements of the US and UK markets under extreme Asian markets.

Keywords: Multivariate density estimation; Nonparametric estimation; Copula; Kullback–Leibler information criterion (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X14002656
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:135:y:2015:i:c:p:71-88

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2014.11.010

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().