  In Ruckdeschel[10], we derive an asymptotic expansion of the maximal mean
squared error (MSE) of location M-estimators on suitably thinned out, shrinking
gross error neighborhoods. In this paper, we compile several consequences of
this result:
  With the same techniques as used for the MSE, we determine higher order
expressions for the risk based on over-/undershooting probabilities as in
Huber[68] and Rieder[80b], respectively.
  For the MSE problem, we tackle the problem of second order robust optimality:
In the symmetric case, we find the second order optimal scores again of Hampel
form, but to an O(n^{-1/2})-smaller clipping height c than in first order
asymptotics. This smaller c improves MSE only by LO(1/n). For the case of
unknown contamination radius we generalize the minimax inefficiency introduced
in Rieder et al. [08] to our second order setup. Among all risk maximizing
contaminations we determine a "most innocent" one. This way we quantify the
"limits of detectability" in Huber[97]'s definition for the purposes of
robustness.
