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On Some Goodness-Of-Fit Tests for Copulas

On Some Goodness-Of-Fit Tests for Copulas


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About the Book

This dissertation, "On Some Goodness-of-fit Tests for Copulas" by Wei, Lu, 吕薇, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Copulas have been known in the statistical literature for many years, and have become useful tools in modeling dependence structure of multivariate random variables, overcoming some of the drawbacks of the commonly-used correlation measures. Goodness-of-fit tests for copulas play a very important role in evaluating the suitability of a potential input copula model. In recent years, many approaches have been proposed for constructing goodness-of-fit tests for copula families. Among them, the so-called "blanket tests" do not require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on. As preliminaries, some background and related results of copulas are firstly presented. Three goodness-of-fit test statistics belonging to the blanket test classification are then introduced. Since the asymptotic distributions of the test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically the effect of low dependence on the empirical sizes and powers of the three blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests for higher dimensional copulas, the simulation studies are extended to some three-dimensional copulas. Finally the three goodness-of-fit tests are applied to two real data sets. DOI: 10.5353/th_b4784996 Subjects: Copulas (Mathematical statistics) Goodness-of-fit tests


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Product Details
  • ISBN-13: 9781361292426
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 120
  • Weight: 572 gr
  • ISBN-10: 1361292423
  • Publisher Date: 26 Jan 2017
  • Binding: Hardback
  • Language: English
  • Spine Width: 8 mm
  • Width: 216 mm


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