Robust estimation for multivariate data

CLAUDIO AGOSTINELLI; RICARDO A. MARONNA; VÍCTOR J. YOHAI

Antalya, Turquia

Conferencia; International Conference onRobust Statistics 2008; 2008

Cukurova University, Turquía

 In Alqallaf, Van Aelst, Yohai and Zamar (2008) a new contamination model, called independent contamination model, is introduced. In this model each component of a multivariate observation has a given probability   of being replaced by an outlier. Then even if  probability that one  component be contaminated   is small, the fraction of observations with at least one contaminated component tends to one when the the dimension of the data p increases. Alqallaf et al. (2008) showed that for this type of contamination the breakdown point of the usual a±ne equivariant robust methods for estimating multivariate location tends to 0 when p increases. A similar result can be proved for a±ne equivariant robust estimates of the scatter matrix. Scatter estimates which are robust for the independent contamination model can be obtained using separate robust estimates of the covariances of each pair of variables. A shortcoming of this approach is that the resulting covariance matrix may not be positive de¯nite. This is specially true in the presence of outliers. In this talk we will present a new kind of robust procedures for estimating the covariance matrix which are related to the composite likelihood methods introduced by Lindsey (1988).