## The Annals of Statistics

### On Local and Nonlocal Measures of Efficiency

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350601

Digital Object Identifier
doi:10.1214/aos/1176350601

Mathematical Reviews number (MathSciNet)
MR913565

Zentralblatt MATH identifier
0651.62040

JSTOR

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

#### Citation

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