| Issue |
ESAIM: PS
Volume 24, 2020
|
|
|---|---|---|
| Page(s) | 842 - 882 | |
| DOI | https://doi.org/10.1051/ps/2020021 | |
| Published online | 24 November 2020 | |
Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments
1
Institut de Mathématiques de Toulouse, UMR5219; Université de Toulouse, CNRS, UT3,
F-31062
Toulouse, France.
2
Institut de Mathématiques de Toulouse, UMR5219; Université de Toulouse, CNRS, UT2J,
F-31058
Toulouse, France.
3
Faculty of Mathematics & Computer Science, University of Science, VNU-HCMC, Ho Chi Minh City, Viet Nam; Vietnam National University,
Ho Chi Minh City, Viet Nam.
* Corresponding author: lagnoux@univ-tlse2.fr
Received:
20
December
2019
Accepted:
3
September
2020
We consider the semi-parametric estimation of the scale parameter of the variogram of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based both on quadratic variations and the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with asymptotic normality results, for a large class of Gaussian processes. We allow for general mean functions, provide minimax upper bounds and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict the finite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.
Mathematics Subject Classification: 60G15 / 62F12
Key words: Gaussian processes / semi-parametric estimation / quadratic variations / scale covariance parameter / asymptotic normality / moment method / minimax upper bounds / aggregation of estimators
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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