The authors consider multivariate analysis of variance procedures based on the multivariate spatial ranks. Two models are considered: the location-family model and the fully nonparametric model. Procedures for testing main and interaction effects are given for the 2 × 2 layout.
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References
1.
Akritas, Michael G.1990. “The Rank Transform Method in Some Two-Factor Designs.”Journal of the American Statistical Association85:73-78.
2.
Akritas, Michael G.
and Steven F. Arnold. 1994. “Fully Nonparametric Hypotheses for Factorial Designs: I. Multivariate Repeated Measures Designs.”Journal of the American Statistical Association89:336-343.
3.
Chaudhuri, Probal
. 1996. “On a Geometric Notion of Quantiles for Multivariate Data.”Journal of the American Statistical Association91:862-872.
4.
Choi, Kyungmee
and John I. Marden. 1997. “An Approach to Multivariate Rank Tests in Multivariate Analysis of Variance.”Journal of the American Statistical Association92:1581-1590.
5.
Gibbons, Jean D.
and Subhabrata Chakraborti. 1992. Nonparametric Statistical Inference. New York: Marcel Dekker.
6.
Hettmansperger, Thomas P.
and Joseph W. McKean. 1998. Robust Nonparametric Statistical Methods. London: Arnold.
7.
Koltchinskii, Vladimir I.1997. “M-estimation, Convexity and Quantiles.”Annals of Statistics25:435-477.
8.
Marden, John I.
and Maria E. T. Muyot. 1995. “Rank Tests for Main and Interaction Effects in Analysis of Variance.”Journal of the American Statistical Association90:1388-1398.
9.
Möttönen, Jyrki
and Hannu Oja. 1995. “Multivariate Spatial Sign and Rank Methods.”Nonparametric Statistics5:201-213.
10.
Munzel, Ullrich
and Edgar Brunner. 2000. “Nonparametric Methods in Multivariate Factorial Designs.”Journal of Statistical Planning and Inference88:117-132.
11.
Patel, Kantilal M.
and David G. Hoel. 1973. “A Nonparametric Test for Interaction in Factorial Experiments.”Journal of the American Statistical Association68:615-620.
12.
Puri, Madan Lal
and Pranab Kumar Sen. 1971. Nonparametric Methods in Multivariate Analysis. New York: John Wiley.
13.
Seber, George A. F.1984. Multivariate Observations. New York: John Wiley.
14.
Small, Christopher G.1990. “A Survey of Multidimensional Medians.”International Statistical Review58:263-277.
