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Adaptive Series Estimators for Copula Densities

In this thesis, based on an orthonormal series expansion, we propose a new nonparametric method to estimate copula density functions. Since the basis coefficients turn out to be expectations, empirical averages are used to estimate these coefficients. We propose estimators of the variance of the estimated basis coefficients and establish their consistency. We derive the asymptotic distribution of the estimated coefficients under mild conditions. We derive a simple oracle inequality for the copula density estimator based on a finite series using the estimated coefficients. We propose a stopping rule for selecting the number of coefficients used in the series and we prove that this rule minimizes the mean integrated squared error. In addition, we consider hard and soft thresholding techniques for sparse representations. We obtain oracle inequalities that hold with prescribed probability for various norms of the difference between the copula density and our threshold series density estimator. Uniform confidence bands are derived as well. The oracle inequalities clearly reveal that our estimator adapts to the unknown degree of sparsity of the series representation of the copula density. A simulation study indicates that our method is extremely easy to implement and works very well, and it compares favorably to the popular kernel based copula density estimator, especially around the boundary points, in terms of mean squared error. Finally, we have applied our method to an insurance dataset. After comparing our method with the previous data analyses, we reach the same conclusion as the parametric methods in the literature and as such we provide additional justification for the use of the developed parametric model. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of
Doctor of Philosophy. / Summer Semester, 2009. / April 30, 2009. / Copula, Nonparametric Estimation, Copula Density / Includes bibliographical references. / Marten Wegkamp, Professor Directing Dissertation; Robert A. van Engelen, Outside Committee Member; Xufeng Niu, Committee Member; Fred Huffer, Committee Member.

Identiferoai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_254259
ContributorsGui, Wenhao (authoraut), Wegkamp, Marten (professor directing dissertation), Van Engelen, Robert A. (outside committee member), Niu, Xufeng (committee member), Huffer, Fred (committee member), Department of Statistics (degree granting department), Florida State University (degree granting institution)
PublisherFlorida State University, Florida State University
Source SetsFlorida State University
LanguageEnglish, English
Detected LanguageEnglish
TypeText, text
Format1 online resource, computer, application/pdf
RightsThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.

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