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

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MANOVA Test Statistics,or Lawley–Hotelling criterion, .), the likelihood-ratio criterion . and the Bartlett–Nanda–Pillai criterion . in the MANOVA model when the sample size is large. The results for . and . are obtained by expressing these statistics in terms of a multivariate scale mixture, and using error bounds evalua

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Gaussian Comparison and Anti-concentration, The key property of these bounds is that they are dimension-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements and on the norm of the mean shift. The obtained bounds significantly improve the bound based on the Pinsker inequality vi

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,Approximations for Statistics Based on Random Sample Sizes,perties of the statistics can be radically changed when the non-random sample size is replaced by a random value. In this chapter, we consider the second-order Chebyshev–Edgeworth type and Cornish–Fisher type expansions based on Student’s .- and Laplace distributions and their quantiles for samples

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Yasunori Fujikoshi,Vladimir V. Ulyanov49]. Aus einer Sekundärquelle kennt man Wasseruhren des zu seiner Zeit berühmten Mechanikers Ktesibios, die wahrscheinlich ein Regelprinzip enthielten. Die Beschreibung in der erhaltenen Sekundärquelle ist leider unklar, so daß die Deutungen zum Teil auseinandergehen. Die Aufgabe der Apparatur war e