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A Test for a Change Point in a Parametric Model Based on a Maximal Wald-Type Statistic

D. L. Hawkins
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 49, No. 3 (Oct., 1987), pp. 368-376
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050660
Page Count: 9
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A Test for a Change Point in a Parametric Model Based on a Maximal Wald-Type Statistic
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Abstract

A large-sample test for a change in the parameter of a parametric model is studied. The test statistic is a maximal Wald-type statistic based on the difference in the maximum likelihood estimator calculated from $X_{1},.\,..,X_{k}$ and $X_{k+1},.\,..,X_{n}$. The asymptotic null distribution is obtained via weak convergence of an empirical process to the standardized tied-down Bessel process. The local power function is obtained in terms of the first-crossing probability of a drifted version of this process.

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