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Secure parameter estimation: Fundamental tradeoffs

The problem of parameter estimation in an adversarial setting, in which an active adversary might decide to compromise the data for the purpose of subverting the estimation decisions, is considered. Forming secure estimation decisions entails two intertwined inference decisions. Specifically, on one hand, deciding whether the data is compromised, like any detection decision, is never perfect. On the other hand, missing any attack translates to degradation in the estimation quality. Based on these two observations, the paper aims to characterize the interplay between two figures of merit q and ß, where q captures how much estimation quality degrades when the objective is to miss the presence of an attacker with a probability not exceeding ß. The paper characterizes the optimal decision rules and compares the results with the existing literature.