Semi-parametric estimation of the variogram of a Gaussian process with stationary increments

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with...

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Bibliographic Details
Published inESAIM. Proceedings and surveys no. 24; pp. 842 - 882
Main Authors Azaïs, Jean-Marc, Bachoc, François, Lagnoux, Agnès, Nguyen, Thi Mong Ngoc
Format Journal Article
LanguageEnglish
Published EDP Sciences 2020
Subjects
Mathematics
Statistics
asymptotic normality
scale covariance parameter
moment method
aggregation of estimators
quadratic variations
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Summary:We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on 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 and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict thefinite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.
ISSN:2267-3059
2267-3059