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<p>In this paper, we study asymptotic properties of the approximated maximum likelihood estimator (MLE) for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations. By the change of measure method and asymptotic analysis technique, we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE. Then, the Cramér-type moderate deviation can be obtained. As applications, the global and local powers for the hypothesis test are shown to approach one at exponential rates. Simulation experiments are conducted to confirm the theoretical results.</p>

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Berry-Esseen Bound and Cramér-Type Moderate Deviation of the MLE for Ornstein-Uhlenbeck Process with Discrete Observations

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Hui Jiang,
  • Xiyao Zhang

摘要

In this paper, we study asymptotic properties of the approximated maximum likelihood estimator (MLE) for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations. By the change of measure method and asymptotic analysis technique, we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE. Then, the Cramér-type moderate deviation can be obtained. As applications, the global and local powers for the hypothesis test are shown to approach one at exponential rates. Simulation experiments are conducted to confirm the theoretical results.