The Annals of Statistics
- Ann. Statist.
- Volume 15, Number 4 (1987), 1401-1420.
On Local and Nonlocal Measures of Efficiency
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.
Ann. Statist., Volume 15, Number 4 (1987), 1401-1420.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.aos/1176350601