Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t, , (P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(, r.) (dx) as an estimate for J xP...
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