On Local and Nonlocal Measures of Efficiency
Wilbert C. M. Kallenberg, Teresa Ledwina
The Annals of Statistics · 1987 · Volume 15 · Issue 4
Abstract
General results on the limiting equivalence of local and nonlocal measures of efficiency are obtained. Why equivalence occurs in so many testing and estimation problems is clarified. Uniformity of the convergence is a key point. The concepts of Frechet- 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. As a second application, the relation between the inaccuracy rate and the asymptotic variance of $L$-estimators is investigated.
Keywords
$L$-estimators, 60F10, 62G20, asymptotic variance, Exact Bahadur efficiency, Frechet-type differentiability, Hadamard-type differentiability, inaccuracy rate, large deviations, Linear rank statistics, Pitman efficiency
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