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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 if ± θ n d θ as n →∞ . And any particular estimate T is said to be unbiased for θ if 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,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/21/2010 for the course STA sta261 taught by Professor Brenner during the Spring '10 term at University of Toronto- Toronto.

Ask a homework question - tutors are online