Multidimensional outlier-proneness of dependent data and the extremal index

Abstract

Listen

Translate article

Let ( Θ n , R n ) be the polar representation of X n , n ≥ 1 , with values in R d . We quantify the outlier-proneness of the sequence X = { X n } n ≥ 1 by ordering its variables according to the values of F Θ n ( R n ) , n ≥ 1 , and by defining two sequences of outlier-proneness coefficients. Such coefficients take into account the clustering of probability level surfaces F θ − 1 ( F Θ n ( R n ) ) , containing or contained in normalized probability level surfaces for the underlying distribution of X , and let us view the extremal index as an indicator of the outlier-proneness of a multidimensional sequence. We illustrate the results with bivariate Gaussian processes with different outlier-proneness.