On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models
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.
Year of publication: |
1996
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Authors: | Gombay, Edit ; Horváth, Lajos |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 56.1996, 1, p. 120-152
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Publisher: |
Elsevier |
Keywords: | likelihood ratio processes maximum likelihood estimators weighted approximations extreme value Brownian bridge (null) |
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