Global smoothness estimation of a Gaussian process from regular sequence designs

Abstract : We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, $r_{\scriptscriptstyle 0}\in \mathds{N}_0$ and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with $X^{(r_{\scriptscriptstyle 0})}$ (the mean-square derivative of $X$ if $r_{\scriptscriptstyle 0}\ge 1$) supposed to be locally stationary with index $\beta_{\scriptscriptstyle 0}$$. From the behavior of quadratic variations built on divided differences of $X$, we derive an estimator of $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$ based on - not necessarily equally spaced - observations of $X$. Various numerical studies of these estimators exhibit their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.
Type de document :
Pré-publication, Document de travail
28 pages. 2014
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https://hal.archives-ouvertes.fr/hal-00750409
Contributeur : Delphine Blanke <>
Soumis le : mercredi 8 janvier 2014 - 21:30:20
Dernière modification le : lundi 20 mars 2017 - 13:46:00
Document(s) archivé(s) le : mercredi 9 avril 2014 - 03:35:15

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  • HAL Id : hal-00750409, version 2
  • ARXIV : 1211.2763

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Delphine Blanke, Céline Vial. Global smoothness estimation of a Gaussian process from regular sequence designs. 28 pages. 2014. <hal-00750409v2>

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