Multivariate Normality Tests Based on Principal Components

On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality

It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...

MVN package: Multivariate Normality Tests

Assessing the assumption of multivariate normality is required by many parametric multivariate statistical methods, such as discriminant analysis, principal component analysis, MANOVA, etc. Here, we present an R package to asses multivariate normality. The MVN package contains three most widely used multivariate normality tests, including Mardia’s, Henze-Zirkler’s and Royston’s multivariate nor...

A Class of Tests for Multivariate Normality Based on Linear Functions of Order Statistics

Principal components for multivariate functional data

A principal component method for multivariate functional data is proposed. Data can be arranged in a matrix whose elements are functions so that for each individual a vector of p functions is observed. This set of p curves is reduced to a small number of transformed functions, retaining as much information as possible. The criterion to measure the information loss is the integrated variance. Un...

Optimal Rank-Based Tests for Common Principal Components

This paper provides optimal testing procedures for the m-sample null hypothesis of Common Principal Components (CPC) under possibly non Gaussian and heterogenous elliptical densities. We first establish, under very mild assumptions that do not require finite moments of order four, the local asymptotic normality (LAN) of the model. Based on that result, we show that the pseudo-Gaussian test prop...