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This is almost selfcontained explanation of our recent result. The contents are based on our talk in the RIMS2014 conference.
Recently, many fundamental and important results in statistical decision theory have been extended to the quantum system. Quantum HuntStein theorem and quantum locally asymptotic normality are typical successful examples.
In our recent preprint, we show quantum minimax theorem, which is also an extension of a wellknown result, minimax theorem in statistical decision theory, first shown by Wald and generalized by LeCam. Our assertions hold for every closed convex set of measurements and for general parametric models of density operator. On the other hand, Bayesian analysis based on least favorable priors has been widely used in classical statistics and is expected to play a crucial role in quantum statistics. According to this trend, we also show the existence of least favorable priors, which seems to be new even in classical statistics.
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