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Published in:
Non-Asymptotic Bounds Read chapter Read first chapter

2020 | OriginalPaper | Chapter

2. Scale-Mixed Distributions

Authors : Yasunori Fujikoshi, Vladimir V. Ulyanov

Published in: Non-Asymptotic Analysis of Approximations for Multivariate Statistics

Publisher: Springer Singapore

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Abstract

In this chapter we present a general theory of approximation of scale-mixed distributions or distributions of scale mixtures, including simple examples of Student’s t-distribution and F-distribution as a scale mixtures of the normal and chi-square distribution, respectively. Such scale mixtures appear as sampling distributions of various statistics such as the studentized version of some estimators. Errors of the approximation are evaluated in \(\sup \) and \(L_1\)-norms. Extension to multivariate scale mixtures with error bounds evaluated in \(L_1\)-norm shall be discussed in Chap. 3.

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previous chapter Non-Asymptotic Bounds
next chapter MANOVA Test Statistics
Literature
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Fujikoshi, Y. (1985). An error bound for an asymptotic expansion of the distribution function of an estimate in a multivariate linear model. The Annals of Statistics, 13, 827–831.MathSciNetCrossRef
2.
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8.
Shimizu, R., & Fujikoshi, Y. (1997). Sharp error bounds for asymptotic expansions of the distribution functions of scale mixtures. Annals of the Institute of Statistical Mathematics, 49, 285–297.MathSciNetCrossRef
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Metadata
Title
Scale-Mixed Distributions
Authors
Yasunori Fujikoshi
Vladimir V. Ulyanov
Copyright Year
2020
Publisher
Springer Singapore
Book
Non-Asymptotic Analysis of Approximations for Multivariate Statistics

Print ISBN: 978-981-13-2615-8

Electronic ISBN: 978-981-13-2616-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-13-2616-5_2

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