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

Katerina Papagiannouli ()
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Katerina Papagiannouli: Humboldt Universität zu Berlin

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 3, No 5, 505-535

Abstract: Abstract 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.

Keywords: Multi-dimensional Lévy processes; Adaptive estimation; Lepskitype rule; Balancing principle; Statistical inference covariance (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09264-2

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