Abstract
Abstract We study a class of asymptotic tests for detecting various types of gradual changes in a location model. The results of Jaruskova (1998. J. Statist. Plann. Inference 70, 263–276) and Huskova (1998. In: Szyszkowicz, B. (Ed.), Asymptotic Methods in Probability and Statistics. Elsevier, Amsterdam, pp. 577–584.) are extended to other families of change alternatives. Under the null hypothesis of “no change”, limiting extreme value distributions of Gumbel type are derived for some asymptotic log-likelihood ratio test statistics. Consistency under certain alternatives is also discussed.
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