EFFICIENCY OF ESTIMATORS FOR LOCALLY ASYMPTOTICALLY NORMAL QUANTUM STATISTICAL MODELS
成果类型：
Article
署名作者：
Fujiwara, Akio; Yamagata, Koichi
署名单位：
University of Osaka; Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/23-AOS2285
发表日期：
2023
页码：
1159-1182
关键词：
摘要：
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.