This research will look at robust estimation of multivariate location and dispersion. The standard classical estimators are the sample mean vector and sample covariance matrix. The affine equivariant M-estimator is robust but has several unresolved problems associated with it. Direct efforts to solve the problems of nonuniqueness for finite sample sizes and lack of a convergent algorithm to find these estimates have failed. The investigator proposes two stage estimators to circumvent these difficulties. The second problem is of identifying non-elliptical point clouds based on the robust residuals. Emphasis will be placed on detecting data sets which cause the breakdown of the M- estimators. The investigator also suggests to study the efficiencies of M-estimators and the higher breakdown statistics under a non- i.i.d. setting.
