2018/06/08 by Jean‐Marc Azäis, Azaïs, Jean-Marc, François Bachoc +5
Computer Science · Mathematics · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Point processes and geometric inequalities #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1806.03135
openalex publication_date 2018/06/08 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28
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.