Titlebook: Non-Asymptotic Analysis of Approximations for Multivariate Statistics; Yasunori Fujikoshi,Vladimir V. Ulyanov Book 2020 The Author(s), und

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General Approach to Constructing Non-Asymptotic Bounds,ing the case of dependent summands and the case when the distributions of weighted sums are approximated by the normal distribution with accuracy of order .. We consider also applications for distributions of .-statistics of the second order and higher.

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Likelihood Ratio Tests with Box-Type Moments,l populations. First, their large-sample approximation method is explained. Then, we derive their high-dimensional asymptotic expansions. Further, it is noted that an error bound for high-dimensional asymptotic expansions can be derived for some statistics including the lambda distribution.

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978-981-13-2615-8The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

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Non-Asymptotic Analysis of Approximations for Multivariate Statistics978-981-13-2616-5Series ISSN 2191-544X Series E-ISSN 2191-5458

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Non-Asymptotic Bounds,e precisely, such statistical statements are evaluated when . and/or . tend to infinity. On the other hand, “non-asymptotic” results are derived under the condition that ., ., and the parameters involved are fixed. In this chapter, we explain non-asymptotic error bounds, while giving the Edgeworth e