×

Multivariate spatial sign and rank methods. (English) Zbl 0857.62056

Summary: Rotation invariant multivariate spatial sign and rank tests and corresponding rotation equivariant estimates based on \(L_1\) type objective functions with Euclidean distance are considered. Multivariate spatial analogues of sign and rank concepts, one- and two-sample sign test, Wilcoxon rank sum and signed rank tests, median and Hodges-Lehmann estimates are reviewed and discussed. Connections with other generalization are considered. The testing theory is illustrated by two examples.

MSC:

62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Arnold, S. F. 1981. ”The Theory of Linear Models and Multivariate Analysis”. New York: Wiley. · Zbl 0514.62069
[2] DOI: 10.1080/02331889008802260 · Zbl 0714.62048
[3] DOI: 10.1007/BF00773354 · Zbl 0799.62061
[4] Brown B. M., J. Roy. Statist. Soc. Ser 45 pp 25– (1983)
[5] Brown B. M., In Encyclopedia of Statistical Sciences 8 pp 574– (1988)
[6] Brown B. M., J. Roy. Statist. Soc. Ser 49 pp 301– (1987)
[7] Brown B. M., Statistical data analysis based on the L1 norm and related methods pp 333– (1987)
[8] Brown B. M., J. Roy. Statist. Soc. Ser 51 pp 117– (1989)
[9] DOI: 10.2307/2290460 · Zbl 0763.62026
[10] DOI: 10.1214/aos/1176348662 · Zbl 0762.62013
[11] Chaudhuri P., To appear in J. Amer. Statist. Assoc 20 (1995)
[12] DOI: 10.2307/2347150
[13] Hettmansperger T. P., L1 -statistical Analysis and Related Methods pp 267– (1992)
[14] Hettmansperger T. P., J. Roy. Statist. Soc. Ser 56 pp 221– (1994)
[15] Hettmansperger T. P., J. Roy. Statist. Soc. Ser 56 pp 235– (1994)
[16] DOI: 10.1080/10485259408832600 · Zbl 1380.62192
[17] Möttönen J., On the efficiency of spatial rank methods submitted (1995)
[18] DOI: 10.1016/0167-7152(83)90054-8 · Zbl 0517.62051
[19] DOI: 10.2307/2290081 · Zbl 0702.62039
[20] Randles R. H., L1 – Statistical Analysis and Related Methods pp 295– (1992)
[21] DOI: 10.1080/03610929008830439 · Zbl 04501353
[22] Rao C.R., Sankhyä 50 pp 289– (1988)
[23] DOI: 10.2307/1403809
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.