TY - GEN
T1 - Rank-based inference for multivariate data in factorial designs
AU - Bathke, Arne C.
AU - Harrar, Solomon W.
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
UR - http://www.scopus.com/inward/record.url?scp=84990036840&partnerID=8YFLogxK
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U2 - 10.1007/978-3-319-39065-9_7
DO - 10.1007/978-3-319-39065-9_7
M3 - Conference contribution
AN - SCOPUS:84990036840
SN - 9783319390635
T3 - Springer Proceedings in Mathematics and Statistics
SP - 121
EP - 139
BT - Robust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions
A2 - McKean, Joseph W.
A2 - Liu, Regina Y.
T2 - International Conference on Robust Rank-Based and Nonparametric Methods, 2015
Y2 - 9 April 2015 through 10 April 2015
ER -