Nearly Optimal Robust Mean Estimation via Empirical Characteristic Function

04/05/2020

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by   Sohail Bahmani, et al.

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We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that the proposed estimator achieves a nearly optimal rate. Furthermore, we show robustness of the estimator against adversarial contamination.