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<p>This paper deals with parameter estimation of the drift coefficient, denoted <i>θ</i>, for a fractional Ornstein-Uhlenbeck process observed at high frequency. Specifically, we provide an estimator of <i>θ</i>, namely <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>θ</mi> <mo>˜</mo> </mover> <mi>n</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$\widetilde{\theta }_{n}$</EquationSource> </InlineEquation>, using the second moment method. We develop some novel estimates to derive an explicit Berry–Esseen bound in the Wasserstein distance for the normal approximation of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>θ</mi> <mo>˜</mo> </mover> <mi>n</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$\widetilde{\theta }_{n}$</EquationSource> </InlineEquation>. Moreover, we prove that our estimate is strictly sharper than the one obtained in Douissi et al. (Electron. J. Stat. 16(1):636–670, <CitationRef CitationID="CR10">2022</CitationRef>).</p>

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Improved Berry-Esseen bounds for parameter estimation of a fractional Ornstein-Uhlenbeck process observed at high frequency

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  • 发表日期：

    2026年1月29日

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  • Fares Alazemi,
  • Khalifa Es-Sebaiy,
  • Mishari Al-Foraih

摘要

This paper deals with parameter estimation of the drift coefficient, denoted θ, for a fractional Ornstein-Uhlenbeck process observed at high frequency. Specifically, we provide an estimator of θ, namely θ ˜ n $\widetilde{\theta }_{n}$ , using the second moment method. We develop some novel estimates to derive an explicit Berry–Esseen bound in the Wasserstein distance for the normal approximation of θ ˜ n $\widetilde{\theta }_{n}$ . Moreover, we prove that our estimate is strictly sharper than the one obtained in Douissi et al. (Electron. J. Stat. 16(1):636–670, 2022).