A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covarianc...

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Bibliographic Details
Published in:Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems 2022-10, Vol.25 (3), p.505-535
Main Author: Papagiannouli, Katerina
Format: Article
Language:English
Subjects:
Covariance
Estimation
Mathematics
Mathematics and Statistics
Minimax technique
Parameters
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Stochastic processes
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Summary:We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.
ISSN:1387-0874
1572-9311
DOI:10.1007/s11203-021-09264-2