The Annals of Statistics

On Local and Nonlocal Measures of Efficiency

Wilbert C. M. Kallenberg and Teresa Ledwina

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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.

Article information

Ann. Statist., Volume 15, Number 4 (1987), 1401-1420.

First available in Project Euclid: 12 April 2007

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Primary: 62G20: Asymptotic properties
Secondary: 60F10: Large deviations

Exact Bahadur efficiency Pitman efficiency inaccuracy rate asymptotic variance large deviations Frechet-type differentiability Hadamard-type differentiability linear rank statistics $L$-estimators


Kallenberg, Wilbert C. M.; Ledwina, Teresa. On Local and Nonlocal Measures of Efficiency. Ann. Statist. 15 (1987), no. 4, 1401--1420. doi:10.1214/aos/1176350601.

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