Semiparametric Multivariate Density Estimation Using Copulas and Shape-Constraints

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dc.contributor.advisorJankowski, Hanna
dc.contributor.authorBoonpatcharanon, Sawitree
dc.date.accessioned2019-11-22T18:46:44Z
dc.date.available2019-11-22T18:46:44Z
dc.date.copyright2019-05
dc.date.issued2019-11-22
dc.date.updated2019-11-22T18:46:44Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractMaximum likelihood estimation of a log-concave density has certain advantages over other nonparametric approaches, such as kernel density estimation, which requires a bandwidth selection. Furthermore, finding the optimal bandwidth gets more difficult as a dimension increases. On the other hand, the shape-constrained approach is automatic and does not need any tuning parameters. However, for both the kernel and log-concave estimators, the rate of convergence slows down as the dimension d increases. To handle this "curse of dimensionality", we study an intermediate semi-parametric copula approach and we estimate the marginals using the log-concave shape-constrained MLE and use a parametric approach to fit the copula parameters. We prove square root n rate of convergence for the parametric estimator and that the joint density converges at a rate of n^(-2/5) regardless of dimension. This is faster than the conjectured rate of n^(-2/(d+4)) for the multivariate log-concave estimators. We examine the performance of our proposed method via simulation studies and real data example.
dc.identifier.urihttp://hdl.handle.net/10315/36721
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectStatistics
dc.subject.keywordssemi-parametric
dc.subject.keywordslog-concave
dc.subject.keywordscopula
dc.subject.keywordsdensity estimation
dc.titleSemiparametric Multivariate Density Estimation Using Copulas and Shape-Constraints
dc.typeElectronic Thesis or Dissertation

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