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.
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DOI : 10.1051/ps/2020021
Mots-clés : Gaussian processes, semi-parametric estimation, quadratic variations, scale covariance parameter, asymptotic normality, moment method, minimax upper bounds, aggregation of estimators
@article{PS_2020__24_1_842_0,
author = {Aza{\"\i}s, Jean-Marc and Bachoc, Fran\c{c}ois and Lagnoux, Agn\`es and Nguyen, Thi Mong Ngoc},
title = {Semi-parametric estimation of the variogram scale parameter of a {Gaussian} process with stationary increments},
journal = {ESAIM: Probability and Statistics},
pages = {842--882},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2020021},
mrnumber = {4178368},
zbl = {1461.60019},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2020021/}
}
TY - JOUR AU - Azaïs, Jean-Marc AU - Bachoc, François AU - Lagnoux, Agnès AU - Nguyen, Thi Mong Ngoc TI - Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments JO - ESAIM: Probability and Statistics PY - 2020 SP - 842 EP - 882 VL - 24 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2020021/ DO - 10.1051/ps/2020021 LA - en ID - PS_2020__24_1_842_0 ER -
%0 Journal Article %A Azaïs, Jean-Marc %A Bachoc, François %A Lagnoux, Agnès %A Nguyen, Thi Mong Ngoc %T Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments %J ESAIM: Probability and Statistics %D 2020 %P 842-882 %V 24 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2020021/ %R 10.1051/ps/2020021 %G en %F PS_2020__24_1_842_0
Azaïs, Jean-Marc; Bachoc, François; Lagnoux, Agnès; Nguyen, Thi Mong Ngoc. Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 842-882. doi : 10.1051/ps/2020021. http://archive.numdam.org/articles/10.1051/ps/2020021/
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