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Testing Epidemic Changes of Infinite Dimensional Parameters

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Abstract

To detect epidemic change in the mean of a sample of size n of random elements in a Banach space, we introduce new test statistics DI based on weighted increments of partial sums. We obtain their limit distributions under the null hypothesis of no change in the mean. Under alternative hypothesis our statistics can detect very short epidemics of length logγ n, γ > 1. We present applications to detect epidemic changes in distribution function or characteristic function of real valued observations as well as changes in covariance matrices of random vectors.

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Authors and Affiliations

  1. Department of Mathematics, Vilnius University and Institute of Mathematics and Informatics, Naugarduko 24, Lt-2006, Vilnius, Lithuania

    Alfredas Račkauskas

  2. Laboratoire P. Painlevé, Université des Sciences et Technologies de Lille, UMR CNRS 8524 Bât. M2, U.F.R. de Mathématiques, F-59655, Villeneuve d’Ascq Cedex, France

    Charles Suquet

Authors
  1. Alfredas Račkauskas
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  2. Charles Suquet
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Correspondence to Charles Suquet.

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Final version 27 October 2004

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Račkauskas, A., Suquet, C. Testing Epidemic Changes of Infinite Dimensional Parameters. Stat Infer Stoch Process 9, 111–134 (2006). https://doi.org/10.1007/s11203-005-0728-5

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  • DOI: https://doi.org/10.1007/s11203-005-0728-5

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