29 definition the sequence of estimators n n 12 is n

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DEFINITION : The sequence of estimators ̂ n : n 1,2,... is n - asymptotically normal if n ̂ n d Normal 0 , C  , all Θ where C is a p p positive semidefinite matrix for all . The matrix C is usually called the asymptotic variance of n ̂ n . Because n ̂ n converges in distribution it is also O p 1 . Therefore, any n -aysmptotically normal estimator is necessarily n -consistent. 30
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