Optimal Unbiased Estimation for Maximal Distribution

Abstract

Unbiased estimation for parameters of maximal distribution is a very fundamental problem in the statistical theory of sublinear expectation. 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 the the lower mean.

References in corpus (4)

• A New Central Limit Theorem under Sublinear Expectations
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
• The Independence under Sublinear Expectations

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