Optimal unbiased estimation for maximal distribution

Hanqing Jin; Shige Peng

doi:10.3934/puqr.2021009

Article Contents

2021, Volume 6, Issue 3: 189-198. Doi: 10.3934/puqr.2021009

This issue Previous Article Reduced-form setting under model uncertainty with non-linear affine intensities Next Article Stein’s method for the law of large numbers under sublinear expectations

Optimal unbiased estimation for maximal distribution

Hanqing Jin^1, and
Shige Peng^2, ,

1.
Mathematical Institute, Oxford University, Oxford, OX1 2JD, United Kingdom
2.
School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Author Bio: E-mail: jinh@maths.ox.ac.uk
E-mail: peng@sdu.edu.cn
E-mail: peng@sdu.edu.cn

Received: April 15, 2021

Accepted: August 09, 2021

Published: September 2021

We thank Dr. Wang Hanchao who provided some very useful suggestions to improve the first draft of this paper. This research is partially supported by Zhongtai Institute of Finance, Shandong University, Tian Yuan Fund of the National Natural Science Foundation of China (Grant Nos. L1624032. and 11526205) and Chinese SAFEA (111 Project) (Grant No. B12023).

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Abstract

Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear expectations. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper mean and the minimum estimator is the smallest unbiased estimator for the lower mean.

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Mathematics Subject Classification: 60E05, 60E07, 60B12.

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References

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