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Maximum likelihood type robust estimates of regression are defined and their asymptotic properties are investigated both theoretically and empirically. Perhaps the most important new feature is that the number p of parameters is allowed to increase with the number n of observations. The initial terms of a formal power series expansion (essentially in powers of p/n) show an excellent agreement with Monte Carlo results, in most cases down to 4 observations per parameter.
Peter J. Huber (Sat,) studied this question.