Statistical Estimation for a Class of Self-Regulating Processes

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...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2015-06, Vol.42 (2), p.485-503
Main Authors: ECHELARD, ANTOINE, VÉHEL, JACQUES LÉVY, PHILIPPE, ANNE
Format: Article
Language:English
Subjects:
Amplitudes
confidence interval
Displacement
Estimating techniques
Estimators
Mathematical analysis
Mathematical models
pointwise regularity
Regularity
Self regulation
self‐regulating function
Statistics
Stochastic processes
strongly consistent estimator
Studies
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Summary: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12118