Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 74-89

BREAKDOWN PROPERTIES OF TWO PROJECTION BASED STATISTICS

By

JIAN ZHANG, Academia Sinica, Beijing and Universite Catholique de Louvain

SUMMARY. In this paper, the sample breakdown points and the asymptotic breakdown points are obtained for two projection based M-statistics of multivariate location. When the function $\rho$, involved in the definitions of these statistics, is strongly redescending, these sample breakdown points will depend on sample, are hard to calculate and their distributions usually provide more information on the robust behavior of the statistics than the asymptotic breakdown points. In this setting, the asymptotic distributions of these sample breakdown points are established. The proof of this result can be used to obtain the null and alternative limit distributions of some projection based multivariate goodness-of-fit test statistics.

AMS (1991) subject classification. 62F35.

Key words and phrases. Projection pursuit, M-estimator, breakdown point, empirical processes.

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