Resistant estimates for high dimensional and functional data based on   random projections
  We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data. 
Ricardo Fraiman and Marcela Svarc
stat.ME