Local and Nonlocal Measures of Efficiency

摘要

Results on the limiting equivalence of local and nonlocal measures of efficiency are obtained. It is clarified why the equivalence occurs in so many testing and estimation problems. Uniformity of the convergence is a key-point. The concepts of Frechet-type and Hadamard-type differentiability, which imply uniformity, play an important role. The theory is applied to tests based on linear rank statistics showing equivalence of the local limit of exact Bahadur efficiency and Pitman efficiency. The relation between the inaccuracy rate and the asymptotic variance of L-estimators is investigated.