Multivariate 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 implement the procedures is documented. The location tests and estimates corresponding to the different score functions (sign, rank, signed rank) are reviewed in the one sample, several samples and multivariate regression cases. Also the tests for sphericity and independence of the random vectors are discussed. The inner standardization of the test statistics is then needed for the affine invariance/equivariance of the methods and it produces the corresponding scatter (or shape) matrix estimate. The main features of the R package SpatialNP is described and its use illustrated with several examples.