Estimating minimum effect with outlier selection

Understand

We introduce one-sided versions of Huber's contamination model, in which corrupted samples tend to take larger values than uncorrupted ones.

• Two intertwined problems are addressed: estimation of the mean of uncorrupted samples (minimum effect) and selection of corrupted samples (outliers).
• Regarding the minimum effect estimation, we derive the minimax risks and introduce adaptive estimators to the unknown number of contaminations.
• Interestingly, the optimal convergence rate highly differs from that in classical Huber's contamination model.