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December, 1987 On Local and Nonlocal Measures of Efficiency
Wilbert C. M. Kallenberg, Teresa Ledwina
Ann. Statist. 15(4): 1401-1420 (December, 1987). DOI: 10.1214/aos/1176350601


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.


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Wilbert C. M. Kallenberg. Teresa Ledwina. "On Local and Nonlocal Measures of Efficiency." Ann. Statist. 15 (4) 1401 - 1420, December, 1987.


Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0651.62040
MathSciNet: MR913565
Digital Object Identifier: 10.1214/aos/1176350601

Primary: 62G20
Secondary: 60F10

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 4 • December, 1987
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