Efficiency of estimators for locally asymptotically normal quantum statistical models
Akio Fujiwara, Koichi Yamagata
The Annals of Statistics · 2023 · Volume 51 · Issue 3
Abstract
We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators, such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105–2141], providing a solid foundation of the theory of weak quantum local asymptotic normality.
Keywords
62A01, 62F12, 81P50, Asymptotic efficiency, asymptotic representation theorem, local asymptotic normality, Minimax estimator, quantum statistics, regular estimator
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