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Statistical Estimation for a Class of Self‐Regulating Processes
Author(s) -
Echelard Antoine,
Véhel Jacques Lévy,
Philippe Anne
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12118
Subject(s) - pointwise , mathematics , estimator , central limit theorem , function (biology) , stochastic process , amplitude , class (philosophy) , midpoint , mathematical analysis , limit (mathematics) , calculus (dental) , statistical physics , statistics , geometry , artificial intelligence , computer science , physics , quantum mechanics , evolutionary biology , biology , medicine , dentistry
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.