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arXiv · 2011.12697

A Lepski\u{i}-type stopping rule for the covariance estimation of multi-dimensional L\'evy processes

Katerina Papagiannouli
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Abstract

We suppose that a L\'evy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepski\u{i}-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.

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Katerina Papagiannouli. 2020-11-25. A Lepski\u{i}-type stopping rule for the covariance estimation of multi-dimensional L\'evy processes. https://arxiv.org/abs/2011.12697

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