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.
"Robust Regression: Asymptotics, Conjectures and Monte Carlo." Ann. Statist. 1 (5) 799 - 821, September, 1973. https://doi.org/10.1214/aos/1176342503