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An exponential nonuniform Berry–Esseen bound of the maximum likelihood estimator in a Jacobi process

Part of: Stochastic analysis Limit theorems

Published online by Cambridge University Press:  14 February 2024

Hui Jiang ,
Qihao Lin  and
Shaochen Wang Open the ORCID record for Shaochen Wang [Opens in a new window]
Hui Jiang*
Affiliation:
Nanjing University of Aeronautics and Astronautics
Qihao Lin*
Affiliation:
Nanjing University of Aeronautics and Astronautics
Shaochen Wang*
Affiliation:
South China University of Technology
*
*Postal address: School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.
*Postal address: School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.
**Postal address: School of Mathematics, South China University of Technology, Guangzhou 510640, China. Email: [email protected]
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Abstract

We establish the exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator of unknown drift parameter in an ultraspherical Jacobi process using the change of measure method and precise asymptotic analysis techniques. As applications, the optimal uniform Berry–Esseen bound and optimal Cramér-type moderate deviation for the corresponding maximum likelihood estimator are obtained.

Keywords

Berry–Esseen boundmaximum likelihood estimatorJacobi processCramér-type moderate deviation

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60F10: Large deviations
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 3 , September 2024 , pp. 909 - 926
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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