Statistical estimation of a class of self-regulating processes

Abstract : 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 miodels for various signals arising e.g. in geophysics and 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 introduced in [4] 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.
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Submitted on : Wednesday, August 20, 2014 - 10:27:25 AM
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Antoine Echelard, Jacques Lévy Véhel, Anne Philippe. Statistical estimation of a class of self-regulating processes. 2014. ⟨hal-00868604v2⟩

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