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ASSIGNMENT%202%20STA261 - STA261 Assignment 2 due...

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STA261 Assignment 2 due: Wed.Mar.31/10 A sequence of statistical estimates θ n with n N is said to be consistent for the parameter θ i ff θ n d θ as n → ∞ . And any particular estimate T is said to be unbiased for θ i ff ET = θ . Thus, unbiasedness is about individual estimators, while consistency is about 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 any unbiased estimate, T , it would be extremely easy to construct a consis- tent sequence θ n from a sample T 1 , . . . , T n IID T ; this is because (by any version of the law of large numbers) we need only take θ n = T = T 1 + · · · + T n n . And this is the chief merit of the property known as unbiasedness — that it 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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