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Statistical Estimation for a Class of Self-Regulating Processes

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  • Antoine Echelard
  • Jacques Lévy Véhel
  • Anne Philippe

Abstract

type="main" xml:id="sjos12118-abs-0001"> Self-regulating processes are stochastic processes whose local regularity, as measured by the pointwise Hölder exponent, is a function of amplitude. They seem to provide relevant models for various signals arising for example in geophysics or biomedicine. We propose in this work an estimator of the self-regulating function (that is, the function relating amplitude and Hölder regularity) of the self-regulating midpoint displacement process and study some of its properties. We prove that it is almost surely convergent and obtain a central limit theorem. Numerical simulations show that the estimator behaves well in practice.

Suggested Citation

  • Antoine Echelard & Jacques Lévy Véhel & Anne Philippe, 2015. "Statistical Estimation for a Class of Self-Regulating Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 485-503, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:485-503
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    File URL: http://hdl.handle.net/10.1111/sjos.12118
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    References listed on IDEAS

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    1. Bardet, Jean-Marc & Surgailis, Donatas, 2013. "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1004-1045.
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