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Aug 22, 2016 at 17:13 comment added Aryeh Kontorovich I presume your goal is to choose a $\hat \mu$ so as to minimize the expected loss w.r.t. to the true $\mu$. The most direct approach would be to minimize the empirical loss and formulate conditions on the distribution that guarantee the convergence of the empirical minimizer to the true value.
Aug 22, 2016 at 16:12 history asked Adrien CC BY-SA 3.0