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2014 | OriginalPaper | Chapter

1. Rank-Based Nonparametrics

Author : Willem R. van Zwet

Published in: Selected Works of Peter J. Bickel

Publisher: Springer New York

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Abstract

Peter Bickel has contributed substantially to the study of rank-based nonparametric statistics. Of his many contributions to research in this area I shall discuss his work on second order asymptotics that yielded surprising results and set off more than a decade of research that deepened our understanding of asymptotic statistics. I shall restrict my discussion to two papers, which are Albers et al. (1976) “Asymptotic expansions for the power of distribution free tests in the one-sample problem” and Bickel (1974) “Edgeworth expansions in nonparametric statistics” where the entire area is reviewed.

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next chapter Robust Statistics
Appendix
Available only for authorised users
Literature
Albers W, Bickel PJ, van Zwet WR (1976) Asymptotic expansions for the power of distribution free tests in the one-sample problem. Ann Stat 4:108–156CrossRefMATH
Albers W, Bickel PJ, van Zwet WR (1978) Correction to asymptotic expansions for the power of distributionfree tests in the one-sample problem. Ann Stat 6:1170CrossRefMATH
Bickel PJ, van Zwet WR (1978) Asymptotic expansions for the power of distribution free tests in the two-sample problem. Ann Stat 6:937–1004CrossRefMATH
Bickel PJ, Goetze F, van Zwet WR (1986) The Edgeworth expansion for U-statistics of degree two. Ann Stat 14:1463–1484CrossRefMATH
Brown LD (1966) On the admissibility of invariant estimators of one or more location parameters. Ann Math Stat 37:1087–1136CrossRefMATH
Cramér H (1937) Random variables and probability distributions. Cambridge tracts in mathematics, vol 36. The University press, Cambridge
Edgeworth FY (1905) The law of error. Proc Camb Philos Soc 20:36–65
Feller W (1966) An introduction to probability theory and its applications, vol II. Wiley, New YorkMATH
Helmers R, van Zwet WR (1982) The Berry-Esseen bound for U-statistics. In: Gupta SS, Berger JO (eds) Statistical decision theory and related topics III, vol 1. Academic, New York, pp 497–512
Hoeffding W (1961) The strong law of large numbers for U-statistics. Institute of statistics, University of North Carolina mimeograph series, vol 302
Stigler SM (1980) Stiglers law of eponymy. Trans New York Acad Sci 39:147–158CrossRef
van Zwet WR (1984) A Berry-Esseen bound for symmetric statistics. Z. Wahrscheinlichkeitstheorie verw Gebiete 66:425–440CrossRefMATH
Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics Bulletin 1(6):80–83CrossRef
Metadata
Title
Rank-Based Nonparametrics
Author
Willem R. van Zwet
Copyright Year
2014
Publisher
Springer New York
Book
Selected Works of Peter J. Bickel

Print ISBN: 978-1-4614-5543-1

Electronic ISBN: 978-1-4614-5544-8

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4614-5544-8_1

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