# Global smoothness estimation of a Gaussian process from regular sequence designs

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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.
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Document type :
Preprints, Working Papers, ...
28 pages. 2014
Domain :

https://hal.archives-ouvertes.fr/hal-00750409
Contributor : Delphine Blanke <>
Submitted on : Wednesday, January 8, 2014 - 9:30:20 PM
Last modification on : Saturday, December 13, 2014 - 1:11:36 AM

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preprint_bv_2014.pdf
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### Identifiers

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

### Citation

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

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