I wanted to use a robust version of covariance and mean. There are many methods like the FastMCD, Olive-Hawkins and DetMCD that achieve this. However, I would like to know how biased is the the final estimate I get.
Have a look at the following paper: Shape Bias of Robust Covariance Estimators: An Empirical Study M. Hubert · P. Rousseeuw · K. Vakili. You can grab a copy here