Affine Invariant Multivariate Rank Tests for Several Samples
نویسندگان
چکیده
Affine invariant analogues of the two-sample Mann-Whitney-Wilcoxon rank sum test and the c-sample Kruskal-Wallis test for the multivariate location model are introduced. The definition of a multivariate (centered) rank function in the development is based on the Oja criterion function. This work extends bivariate rank methods discussed by Brown and Hettmansperger (1987a,b) and multivariate sign methods by Hettmansperger and Oja (1994). The asymptotic distribution theory is developed to consider the Pitman asymptotic efficiencies and the theory is illustrated by an example.
منابع مشابه
Multivariate Generalized Spatial Signed-Rank Methods
New multivariate generalized signed-rank tests for the one sample location model having favorable efficiency and robustness properties are introduced and studied. Limiting distributions of the tests and related estimates as well as formulae for asymptotic relative efficiencies are found. Relative efficiencies with respect to the classical Hotelling T 2 test (and the mean vector) are evaluated f...
متن کاملNonparametric Methods for Multivariate Location Problems with Independent and Cluster Correlated Observations
The aim of this doctoral thesis was to develop efficient nonparametric multivariate methods for independent and identically distributed (i.i.d.) observations and for cluster correlated observations. The first part of the thesis and two of the original articles deal with spatial sign and spatial rank methods, and their affine invariant and equivariant extensions, for the one-sample and the sever...
متن کاملSigned-rank tests for location in the symmetric independent component model
The so-called independent component (IC) model states that the observed p-vectorX is generated via X = ΛZ + μ, where μ is a p-vector, Λ is a full-rank matrix, and the centered random vector Z has independent marginals. We consider the problem of testing the null hypothesis H0 : μ = μ0, where μ0 is a fixed p-vector, on the basis of i.i.d. observations X1, . . . ,Xn generated by the symmetric ver...
متن کاملMultivariate nonparametrical methods based on spatial signs and ranks: The R package SpatialNP
Classical multivariate statistical inference methods are often based on the sample mean vector and covariance matrix. They are then optimal under the assumption of multivariate normality but loose in efficiency in the case of heavy tailed distribution. In this paper nonparametric and robust competitors based on the spatial signs and ranks are discussed and the R statistical software package to ...
متن کاملAn affine invariant multiple test procedure for assessing multivariate normality
Amultiple test procedure for assessing multivariate normality (MVN) that combines a finite set of affine invariant test statistics for MVN is proposed. This combination is based on a method introduced by Fromont and Laurent (Ann. Statist., 680–720, 34, 2006) that can be viewed as an improvement of the classical Bonferroni’s method. The usefulness of such approach is illustrated through a multip...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003