applications of the random projection method
Juan Antonio Cuesta-Albertos
Universidad de Cantabria, Spain
Since our recent paper published in Journal of Theoretical Probability
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.