Economics Commons^™

Equivalence Of The Higher-Order Asymptotic Efficiency Of K-Step And Extremum Statistics, Donald W.K. Andrews

Cowles Foundation Discussion Papers

It is well known that a one-step scoring estimator that starts from any N 1 /2 -consistent estimator has the same first-order asymptotic efficiency as the maximum likelihood estimator. This paper extends this result to k -step estimators and test statistics for k > 1, higher-order asymptotic efficiency, and general extremum estimators and test statistics. The paper shows that a k -step estimator has the same higher-order asymptotic efficiency, to any given order, as the extremum estimator towards which it is stepping, provided (i) k is sufficiently large, (ii) some smoothness and moment conditions hold, and (iii) a condition on the …