A semiparametric maximum likelihood ratio test for the change point in copula models |
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| Institution: | 1. Laboratoire de Mathématiques Appliquées-L.M.A.C., Université de Technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France;2. Laboratoire de Mathématiques de Reims (EA 4535), Université de Reims Champagne-Ardenne. UFR Sciences, Moulin de la Housse, B.P. 1039, 51687 Reims, France;1. School of Statistics, Southwestern University of Finance and Economics, China;2. Department of Mathematical Sciences, Eastern New Mexico University, USA;3. School of Science, Xi’an University of Technology, China;4. Department of Mathematical Sciences, New Mexico State University, USA;1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan St, 322 Science and Engineering Offices, Chicago, IL 60607, United States;2. Department of Statistics, North Carolina State University, 5109 SAS Hall, 2311 Stinson Drive, Raleigh, NC 27695, United States;1. Department of Ophthalmology in the Second Xiangya Hospital, Central South University, Changsha, 410011 Hunan, China;2. Hunan Clinical Research Center of Ophthalmic Disease, Changsha, 410011 Hunan, China;1. University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland;2. School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK;3. Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100 Torun, Poland;1. Department of Biophysics, Johns Hopkins University, Baltimore, MD, USA;2. Department of Bioengineering, University of Illinois, Urbana, IL, USA;1. Ladislaus von Bortkiewicz Chair of Statistics, C.A.S.E.–Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany;2. Chair of Econometrics and Statistics esp. Transportation, Institute of Economics and Transport, Faculty of Transportation, Dresden University of Technology, Helmholtzstrasse 10, 01069 Dresden, Germany |
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| Abstract: | In the present paper, a semiparametric maximum-likelihood-type test statistic is proposed and proved to have the same limit null distribution as the classical parametric likelihood one. Under some mild conditions, the limiting law of the proposed test statistic, suitably normalized and centralized, is shown to be double exponential, under the null hypothesis of no change in the parameter of copula models. We also discuss the Gaussian-type approximations for the semiparametric likelihood ratio. The asymptotic distribution of the proposed statistic under specified alternatives is shown to be normal, and an approximation to the power function is given. Simulation results are provided to illustrate the finite sample performance of the proposed statistical tests based on the double exponential and Gaussian-type approximations. |
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| Keywords: | Dependence function Multivariate rank statistics Semiparametric inference Copulas Change point Likelihood ratio processes Brownian bridge Weighted approximations Extreme value asymptotics |
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