Rank-based inference for multivariate data in factorial designs

Arne C. Bathke; Solomon W. Harrar

doi:10.1007/978-3-319-39065-9_7

Rank-based inference for multivariate data in factorial designs

Arne C. Bathke, Solomon W. Harrar

Dr. Bing Zhang Department of Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

We introduce fully nonparametric, rank-based test statistics for inference on multivariate data in factorial designs, and derive their asymptotic sampling distribution. The focus here is on the asymptotic setting where the number of levels of one factor tends to infinity, while the number of levels of the other factor, as well as the replication size per factor level combination, are fixed. The resulting test statistics can be calculated directly, they don’t involve any iterative computational procedures. To our knowledge, they provide the first viable approach to a fully nonparametric analysis of, for example, multivariate ordinal responses, or a mix of ordinal with other response variables, in a factorial design setting.

Original language	English
Title of host publication	Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions
Editors	Joseph W. McKean, Regina Y. Liu
Pages	121-139
Number of pages	19
DOIs	https://doi.org/10.1007/978-3-319-39065-9_7
State	Published - 2016
Event	International Conference on Robust Rank-Based and Nonparametric Methods, 2015 - Kalamazoo, United States Duration: Apr 9 2015 → Apr 10 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	168
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Robust Rank-Based and Nonparametric Methods, 2015
Country/Territory	United States
City	Kalamazoo
Period	4/9/15 → 4/10/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

Keywords

Asymptotics
Multivariate statistics
Nonparametric method
Ordinal data
Rank test

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-39065-9_7

Cite this

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title = "Rank-based inference for multivariate data in factorial designs",

abstract = "We introduce fully nonparametric, rank-based test statistics for inference on multivariate data in factorial designs, and derive their asymptotic sampling distribution. The focus here is on the asymptotic setting where the number of levels of one factor tends to infinity, while the number of levels of the other factor, as well as the replication size per factor level combination, are fixed. The resulting test statistics can be calculated directly, they don{\textquoteright}t involve any iterative computational procedures. To our knowledge, they provide the first viable approach to a fully nonparametric analysis of, for example, multivariate ordinal responses, or a mix of ordinal with other response variables, in a factorial design setting.",

keywords = "Asymptotics, Multivariate statistics, Nonparametric method, Ordinal data, Rank test",

author = "Bathke, {Arne C.} and Harrar, {Solomon W.}",

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year = "2016",

doi = "10.1007/978-3-319-39065-9_7",

language = "English",

isbn = "9783319390635",

series = "Springer Proceedings in Mathematics and Statistics",

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Bathke, AC & Harrar, SW 2016, Rank-based inference for multivariate data in factorial designs. in JW McKean & RY Liu (eds), Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions. Springer Proceedings in Mathematics and Statistics, vol. 168, pp. 121-139, International Conference on Robust Rank-Based and Nonparametric Methods, 2015, Kalamazoo, United States, 4/9/15. https://doi.org/10.1007/978-3-319-39065-9_7

Rank-based inference for multivariate data in factorial designs. / Bathke, Arne C.; Harrar, Solomon W.
Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions. ed. / Joseph W. McKean; Regina Y. Liu. 2016. p. 121-139 (Springer Proceedings in Mathematics and Statistics; Vol. 168).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Harrar, Solomon W.

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N2 - We introduce fully nonparametric, rank-based test statistics for inference on multivariate data in factorial designs, and derive their asymptotic sampling distribution. The focus here is on the asymptotic setting where the number of levels of one factor tends to infinity, while the number of levels of the other factor, as well as the replication size per factor level combination, are fixed. The resulting test statistics can be calculated directly, they don’t involve any iterative computational procedures. To our knowledge, they provide the first viable approach to a fully nonparametric analysis of, for example, multivariate ordinal responses, or a mix of ordinal with other response variables, in a factorial design setting.

AB - We introduce fully nonparametric, rank-based test statistics for inference on multivariate data in factorial designs, and derive their asymptotic sampling distribution. The focus here is on the asymptotic setting where the number of levels of one factor tends to infinity, while the number of levels of the other factor, as well as the replication size per factor level combination, are fixed. The resulting test statistics can be calculated directly, they don’t involve any iterative computational procedures. To our knowledge, they provide the first viable approach to a fully nonparametric analysis of, for example, multivariate ordinal responses, or a mix of ordinal with other response variables, in a factorial design setting.

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KW - Nonparametric method

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Rank-based inference for multivariate data in factorial designs

Abstract

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Keywords

ASJC Scopus subject areas

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