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On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models

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  • Gombay, Edit
  • Horváth, Lajos

Abstract

We study the asymptotics of maximum-likelihood ratio-type statistics for testing a sequence of observations for no change in parameters against a possible change while some nuisance parameters remain constant over time. We obtain extreme value as well as Gaussian-type approximations for the likelihood ratio. We get necessary and sufficient conditions for the weak convergence of supremum andLp-functionals of the likelihood ration process. We also approximate the maximum likelihood ratio with Ornstein-Uhlenbeck processes and obtain bounds for the rate of approximation. We show that the Ornstein-Uhlenbeck approach is superior to the extreme value limit in case of moderate sample sizes.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 56 (1996)
Issue (Month): 1 (January)
Pages: 120-152

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Handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:120-152

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Related research

Keywords: likelihood ratio processes maximum likelihood estimators weighted approximations extreme value Brownian bridge (null);

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Cited by:
  1. Manner, Hans & Candelon, Bertrand, 2007. "Testing for Asset Market Linkages: A new Approach based on Time-Varying Copulas," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Post-Print halshs-00368334, HAL.
  3. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368334, HAL.
  4. Batsidis, A. & Horváth, L. & Martín, N. & Pardo, L. & Zografos, K., 2013. "Change-point detection in multinomial data using phi-divergence test statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 53-66.
  5. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
  6. Dominique Guegan & Jing Zhang, 2006. "Change analysis of dynamic copula for measuring dependence in multivariate financial data," Post-Print halshs-00189141, HAL.

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