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

Producción científica: Conference contribution › revisión exhaustiva

7 Citas (Scopus)

Resumen

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.

Idioma original	English
Título de la publicación alojada	Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions
Editores	Joseph W. McKean, Regina Y. Liu
Páginas	121-139
Número de páginas	19
DOI	https://doi.org/10.1007/978-3-319-39065-9_7
Estado	Published - 2016
Evento	International Conference on Robust Rank-Based and Nonparametric Methods, 2015 - Kalamazoo, United States Duración: abr 9 2015 → abr 10 2015

Serie de la publicación

Nombre	Springer Proceedings in Mathematics and Statistics
Volumen	168
ISSN (versión impresa)	2194-1009
ISSN (versión digital)	2194-1017

Conference

Conference	International Conference on Robust Rank-Based and Nonparametric Methods, 2015
País/Territorio	United States
Ciudad	Kalamazoo
Período	4/9/15 → 4/10/15

Nota bibliográfica

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

ASJC Scopus subject areas

General Mathematics

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

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@inproceedings{96d7f4ae25a24dbebed42b4138759a47,

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.\}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; International Conference on Robust Rank-Based and Nonparametric Methods, 2015 ; Conference date: 09-04-2015 Through 10-04-2015",

year = "2016",

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

language = "English",

isbn = "9783319390635",

series = "Springer Proceedings in Mathematics and Statistics",

pages = "121--139",

editor = "McKean, \{Joseph W.\} and Liu, \{Regina Y.\}",

booktitle = "Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions",

}

Bathke, AC & Harrar, SW 2016, Rank-based inference for multivariate data in factorial designs. En 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).

Producción científica: Conference contribution › revisión exhaustiva

TY - GEN

T1 - Rank-based inference for multivariate data in factorial designs

AU - Bathke, Arne C.

AU - Harrar, Solomon W.

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

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.

KW - Asymptotics

KW - Multivariate statistics

KW - Nonparametric method

KW - Ordinal data

KW - Rank test

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M3 - Conference contribution

AN - SCOPUS:84990036840

SN - 9783319390635

T3 - Springer Proceedings in Mathematics and Statistics

SP - 121

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BT - Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions

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ER -

Rank-based inference for multivariate data in factorial designs

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ASJC Scopus subject areas

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