The Random Tukey Depth

• Autores: Juan Antonio Cuesta Albertos , Alicia Nieto Reyes
• Localización: XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública: actas, 2007, ISBN 978-84-690-7249-3
• Idioma: inglés
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• Resumen

  • The Tukey depth is a well-known, non-parametric, multidimensional depth which characterizes measures that have a finite support. The Tukey depth of a given point involves a non-denumerable set of projections, and hence, even approximations are not computationally effective.

    Here, we introduce the random Tukey depth. It approximates the Tukey depth using a finite number of randomly chosen projections.

    The random Tukey depth is non-parametric and characterizes atomic measures.

    Its computational time is comparable with the one from Mahalanobis depth.

    Although the randomness may be considered a drawback, as the number of considered projections increases, the random depth does stabilize. The stabilization number, of course, depends on the dimension and sample size but it is surprisingly low. In fact, for samples sizes smaller or equal to 1000, it seems that 36 projections suffice for every dimension.

    We also broaden the random Tukey depth to cover the functional case.

    The presentation will include some simulations and applications to real data sets.