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On Sequential Empirical Distribution Functions for Random Variables with Mean Zero

In: Mathematical Statistics and Limit Theorems

Author

Listed:
  • Erich Haeusler

    (University of Giessen, Mathematical Institute)

  • Stefan Horni

    (University of Giessen, Mathematical Institute)

Abstract

The classical sequential empirical distribution function incorporates all subsamples of a sample of independent and identically distributed random variables and is therefore well suited to construct tests for detecting a distributional change occurring somewhere in the sample. If the independent and identically distributed variables are replaced by the residuals of appropriate time series models tests for a distributional change in the unobservable errors (or innovations) of these models are obtained; see Bai (Annals of Statistics, 22:2051–2061, 1994) for the discussion of ARMA models. These errors are often assumed to have mean zero, an information which is not taken into account by the classical sequential empirical distribution function. Based upon ideas from empirical likelihood, see Owen (London/Boca Raton: Chapman & Hall/CRC, 2001), we consider a modified sequential empirical distribution function for random variables with mean zero which does exploit this information.

Suggested Citation

  • Erich Haeusler & Stefan Horni, 2015. "On Sequential Empirical Distribution Functions for Random Variables with Mean Zero," Springer Books, in: Marc Hallin & David M. Mason & Dietmar Pfeifer & Josef G. Steinebach (ed.), Mathematical Statistics and Limit Theorems, edition 127, pages 125-146, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12442-1_8
    DOI: 10.1007/978-3-319-12442-1_8
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