Smooth optimisation for the MCD estimator

Michaël Schyns

University of Namur, Belgium

The computation of the MCD estimator corresponds to a combinatorial problem: one has to find the subset of h points out of n which minimizes the generalized variance. Enumerating all the possible h-subsets is often infeasible due to the required computation time. Computing this estimator efficiently and in a reasonable time has been a challenge in robust statistics since the definition of this estimator. Many heuristic algorithms have been proposed. These usually consist of random subsampling with some improvement step to get a feasible solution which is not too bad. In this talk, a convex geometry approach is used to define the MCD in a different way, leading to the optimisation of a smooth function under bounds and linear constraints. Some ideas to solve this optimisation problem in an efficient and fast way will be illustrated.


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