An estimator is said to be consistent if for any !0, P( !)
Chapter 6, Problem 6.31(choose chapter or problem)
An estimator is said to be consistent if for any !0, P( !) 0 0 as n 0 . That is, is consistent if, as the sample size gets larger, it is less and less likely that will be further than !from the true value of . Show that X is a consistent estimator of when 2 by using Chebyshevs inequality from Exercise 44 of Chapter 3. [Hint: The inequality can be rewritten in the form P(Y Y!) 2 Y /! Now identify Y with X.] 3
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