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New Kolmogorov bounds in the CLT for random ratios and applications

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  • Es-Sebaiy, Khalifa
  • Alazemi, Fares

Abstract

We develop techniques for determining an explicit Berry–Esseen bound in the Kolmogorov distance for the normal approximation of a ratio of Gaussian functionals. We provide an upper bound in terms of the third and fourth cumulants, using some novel techniques and sharp estimates for cumulants. As applications, we study the rate of convergence of the distribution of discretized versions of minimum contrast and maximum likelihood estimators of the drift parameter of the Ornstein–Uhlenbeck process. Moreover, we derive upper bounds that are strictly sharper than those available in the literature.

Suggested Citation

  • Es-Sebaiy, Khalifa & Alazemi, Fares, 2024. "New Kolmogorov bounds in the CLT for random ratios and applications," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002388
    DOI: 10.1016/j.chaos.2024.114686
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    References listed on IDEAS

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    1. Bishwal, Jaya P.N., 2006. "Rates of weak convergence of approximate minimum contrast estimators for the discretely observed Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1397-1409, July.
    2. Kim, Yoon Tae & Park, Hyun Suk, 2017. "Optimal Berry–Esseen bound for statistical estimations and its application to SPDE," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 284-304.
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