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On Gaussian Compound Poisson Type Limiting Likelihood Ratio Process

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Advances in Theoretical and Applied Statistics

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. Recently it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this chapter we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish that the compound Poisson type likelihood ratio can also be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Blaise Pascal, 63177, Aubière CEDEX, France

    Sergueï Dachian

  2. Department of Information Technology and Mathematical Methods, University of Bergamo, 24044, Dalmine, Italy

    Ilia Negri

Authors
  1. Sergueï Dachian
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  2. Ilia Negri
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Correspondence to Ilia Negri .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Trieste, P.le Europa 1, Trieste, 34127, Italy

    Nicola Torelli

  2. Department of Statistics, University of Padua, Via Cesare Battisti 241, Padova, 35121, Italy

    Fortunato Pesarin

  3. Université Paris Descartes, rue des Saints-Pères 45, Paris, 75270, France

    Avner Bar-Hen

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Dachian, S., Negri, I. (2013). On Gaussian Compound Poisson Type Limiting Likelihood Ratio Process. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds) Advances in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35588-2_4

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