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Robust weighted estimator of location

Now let $W = (w_1, \ldots, w_n), w_i >= 0$ be (non-random) reliability weights. Weighted mean is an example of estimator that takes weights into account, but it is non-robust. … Is there a statistically (like HL-estimator) and computationally efficient ($O(n log(n))$ at least) estimator of sample location that accounts for weights? …
Andrey Paramonov's user avatar