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THE BEHAVIOR OF LOCATION ESTIMATORS UNDER A FIXED DENSITY
THE BEHAVIOR OF LOCATION ESTIMATORS OVER A CLASS OF DENSITIES
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absolutely continuous density adaptive estimators asymptotically optimal Borel measurable Cauchy–Schwarz inequality consequence Cramér–Rao bound Cramér–Rao inequality defined density f e derivative f dichtheid differentiable dominated convergence theorem Egº estimator of location estimator Tn Fatou's lemma finite Fisher information fixed sample Fubini's theorem Furthermore Hence holds implies Laat Lebesgue measure Let f e Let H liminf limsup location estimators loss functions lower bound mators mean square error measurable function n)dn n+oo n1 f obtain Pitman estimator PROOF result ſ f ſ H ſ Hn ſ ſ satisfies score function Section sequence ſº standard normal distribution standard normal random statistical situation subsets sup inf symmetric about zero symmetric distribution function Tn e Tn translation equivariant estimators truncated variance verdeling y-roo zijn