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

Authors
  • Azaïs, Jean-Marc
  • Bachoc, François
  • Klein, Thierry
  • Lagnoux, Agnès
  • Nguyen, Thi Mong Ngoc
Publication Date
Jun 08, 2018
Source
Kaleidoscope Open Archive
Keywords
Language
English
License
Unknown
External links

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 thefinite-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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