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- W1615192910 abstract "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." @default.
- W1615192910 created "2016-06-24" @default.
- W1615192910 creator A5081348946 @default.
- W1615192910 date "2010-06-01" @default.
- W1615192910 modified "2023-09-28" @default.
- W1615192910 title "Consequences of Higher Order Asymptotics for the MSE of M-estimators on Neighborhoods" @default.
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