Computation of Huber's M-estimates for a block-angular regression problem

Huber's M-estimation technique is applied to a block-angular regression problem, which may arise from some applications. A recursive, modified Newton approach to computing the estimates is presented. The structure of the problem is exploited to make the algorithm efficient. It is shown how to efficiently compute a descent search direction by using updating/downdating techniques for matrix factorizations. Numerical test results suggest that the proposed approach is effective.