Multivariate L1 Statistical Methods: The Package MNM

Abstract

In the paper we present an R package MNM dedicated to multivariate data analysis based on the L₁ norm. The analysis proceeds very much as does a traditional multivariate analysis. The regular L₂ norm is just replaced by different L₁ norms, observation vectors are replaced by their (standardized and centered) spatial signs, spatial ranks, and spatial signed-ranks, and so on. The procedures are fairly efficient and robust, and no moment assumptions are needed for asymptotic approximations. The background theory is briefly explained in the multivariate linear regression model case, and the use of the package is illustrated with several examples using the R package MNM.