STA261 Assignment 2due: Wed.Mar.31/10A sequence of statistical estimatesθnwithn∈Nis said to beconsistentforthe parameterθiffθnd→θasn→ ∞.And any particular estimateTis said to beunbiasedforθiffET=θ.Thus, unbiasedness is about individual estimators, while consistency isabout sequences of such. Consistency is certainly the more fundamen-tal (and important) requirement that one would demand of an estima-tion procedure.But it should be clear to the reader that given anyunbiased estimate,T, it would be extremely easy to construct a consis-tent sequenceθnfrom a sampleT1, . . . , TnIID T; this is because (byany version of the law of large numbers) we need only takeθn=T=T1+· · ·+Tnn.And this is the chief merit of the property known as unbiasedness — thatit gives a quick and ready basis for the construction of consistent se-quences.More important for any single estimate,T, than the property of unbi-asedness is just how close it actually is to the parameter,
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