Statistical Estimation for a Class of Self-Regulating Processes

Antoine Echelard, Jacques Lévy Véhel and Anne Philippe

Scandinavian Journal of Statistics, 2015, vol. 42, issue 2, 485-503

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.

Date: 2015
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