On estimation of regularity for Gaussian processes
Résumé
We consider a real Gaussian process $X$ with unknown smoothness $r_0$ where $r_0$ is a nonnegative integer and the mean-square derivative $X^{(r_0)}$ is supposed to be locally stationary of index $\beta_0$. From $n+1$ equidistant observations, we propose and study an estimator of $(r_0,\beta_0)$ based on results for quadratic variations of the underlying process. Various numerical studies of these estimators derive their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.
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