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2014 Global smoothness estimation of a Gaussian process from general sequence designs
Delphine Blanke, Céline Vial
Electron. J. Statist. 8(1): 1152-1187 (2014). DOI: 10.1214/14-EJS925

Abstract

We consider a real Gaussian process $X$ with global unknown smoothness $(r_{\scriptscriptstyle 0},\beta _{\scriptscriptstyle 0}$): more precisely $X^{(r_{\scriptscriptstyle 0})}$, $r_{\scriptscriptstyle 0}\in{\mathds {N}}_{0}$, is supposed to be locally stationary with Hölder exponent $\beta _{\scriptscriptstyle 0}$, $\beta _{\scriptscriptstyle 0}\in]0,1[$. For $X$ observed at a finite set of points, we derive estimators of $r_{\scriptscriptstyle 0}$ and $\beta _{\scriptscriptstyle 0}$ based on the quadratic variations for the divided differences of $X$. Under mild conditions, we obtain an exponential bound for estimating $r_{\scriptscriptstyle 0}$, as well as sharp rates of convergence (up to logarithmic factors) for the estimation of $\beta _{\scriptscriptstyle 0}$. An extensive simulation study illustrates the finite-sample properties of both estimators for different types of processes and we also include two real data applications.

Citation

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Delphine Blanke. Céline Vial. "Global smoothness estimation of a Gaussian process from general sequence designs." Electron. J. Statist. 8 (1) 1152 - 1187, 2014. https://doi.org/10.1214/14-EJS925

Information

Published: 2014
First available in Project Euclid: 12 August 2014

zbMATH: 1298.62141
MathSciNet: MR3263116
Digital Object Identifier: 10.1214/14-EJS925

Subjects:
Primary: 60G15, 62F12, 62M05, 62M09
Secondary: 60G17, 65D05

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 1 • 2014
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