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

Edit Gombay and Lajos Horvath

Journal of Multivariate Analysis, 1996, vol. 56, issue 1, 120-152

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.

Keywords: likelihood; ratio; processes; maximum; likelihood; estimators; weighted; approximations; extreme; value; Brownian; bridge; (null) (search for similar items in EconPapers)
Date: 1996
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