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Mathematical Statistics: Basic Concepts and Theoretical Tools for Finite Sample Analysis

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Book cover Finite Sample Analysis in Quantum Estimation

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In this chapter, we introduce some fundamentals of statistical estimation theory. There are three purposes to this chapter. The first is to set down mathematical preliminaries in order to treat several quantum estimation problems. The second purpose is to explain how to evaluate the estimation errors and the effects of statistical errors on the estimation errors. The third is to explain known results in statistical parameter estimation which have been used in quantum estimation theory or will be used in chapters that follow. In Sect. 3.1, we explain fundamental concepts and technical terms in probability theory and statistical parameter estimation. In Sect. 3.2, we explain some known results in the asymptotic theory. In Sect. 3.3, we explain known results for expected loss and error probability involving finite samples.

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Authors and Affiliations

  1. Department of Physics Graduate School of Science, The University of Tokyo, Tokyo, Japan

    Takanori Sugiyama

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  1. Takanori Sugiyama
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Correspondence to Takanori Sugiyama .

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Sugiyama, T. (2014). Mathematical Statistics: Basic Concepts and Theoretical Tools for Finite Sample Analysis. In: Finite Sample Analysis in Quantum Estimation. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54777-8_3

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