This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Let n be an estimator of based on a sample size of n . The estimator is asymptotically unbiased if lim n E ( n ) = An estimator is (weakly) consistent if, for all > 0 and any , lim n Pr [  n  > ] = 0 A sucient (although not necessary) condition for consistency is that the estimator is asymptotically unbiased and Var ( ) 0. 5 / 7 Mean Squared Error (MSE) The mean squared error (MSE) of an estimator is MSE ( ) = E [(  ) 2 ] Alternatively, it is written as MSE ( ) = [ bias ( )] 2 + Var ( ) 6 / 7 Example (Asymptotic unbiasedness in Uniform) A rv is uniformly distributed on the interval (0 , ) . Consider the estimtor = max( X 1 , ..., X n ) . Show that is asymptotically unbiased Show that is a consistent estimator of Evaluate the MSE of 7 / 7...
View
Full
Document
 Fall '09
 davidlandriault

Click to edit the document details