A spectral algorithm for learning mixture models
Journal of Computer and System Sciences - Special issue on FOCS 2002
A new test for multivariate normality
Journal of Multivariate Analysis
The Tukey and the random Tukey depths characterize discrete distributions
Journal of Multivariate Analysis
On depth measures and dual statistics. A methodology for dealing with general data
Journal of Multivariate Analysis
On projection-based tests for directional and compositional data
Statistics and Computing
Journal of Multivariate Analysis
A random-projection based test of Gaussianity for stationary processes
Computational Statistics & Data Analysis
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The possibility of considering random projections to identify probability distributions belonging to parametric families is explored. The results are based on considerations involving invariance properties of the family of distributions as well as on the random way of choosing the projections. In particular, it is shown that if a one-dimensional (suitably) randomly chosen projection is Gaussian, then the distribution is Gaussian. In order to show the applicability of the methodology some goodness-of-fit tests based on these ideas are designed. These tests are computationally feasible through the bootstrap setup, even in the functional framework. Simulations providing power comparisons of these projections-based tests with other available tests of normality, as well as to test the Black-Scholes model for a stochastic process are presented.