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

Abstract : 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 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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Submitted on : Tuesday, February 12, 2019 - 4:02:30 PM
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  • HAL Id : hal-01802830, version 2
  • ARXIV : 1806.03135

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Jean-Marc Azaïs, François Bachoc, Thierry Klein, Agnès Lagnoux, Thi Mong Ngoc Nguyen. Semi-parametric estimation of the variogram of a Gaussian process with stationary increments. 2019. ⟨hal-01802830v2⟩

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