Some applications of the random projection method

Juan Antonio Cuesta-Albertos

Universidad de Cantabria, Spain

Since our recent paper published in Journal of Theoretical Probability 2007, in which the authors show that a multidimensional or functional probability distribution is almost surely determined by one randomly chosen (one-dimensional) marginal, some papers have appeared proposing simple methods to test several statistical hypotheses.

In this talk we will analyze two of such proposals. First one consists of a simple procedure to test uniformity in spherical (directional) and compositional data, as well as sphericity of the underlying distribution and homogeneity in two-sample problems on the sphere or the simplex. In the second one, we will show how to construct a procedure to handle complicated ANOVA designs for functional data.

The proposed tests have an number of advantages, mostly associated with their flexibility, computational simplicity and ease of application even in high-dimensional cases. Moreover, as far as we know, there is no alternative in the literature which allows to handle those complicated ANOVA designs.

The talk will also include the analysis of some real data sets, as well as some comparisons with other alternative procedure.