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February 2000 Vanishing shortcoming and asymptotic relative efficiency
Tadeusz Inglot, Wilbert C. M. Kallenberg, Teresa Ledwina
Ann. Statist. 28(1): 215-238 (February 2000). DOI: 10.1214/aos/1016120370


The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order efficiency, but in regular cases there is equivalence. The results are in particular applied to tests for goodness-of-it.


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Tadeusz Inglot. Wilbert C. M. Kallenberg. Teresa Ledwina. "Vanishing shortcoming and asymptotic relative efficiency." Ann. Statist. 28 (1) 215 - 238, February 2000.


Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62328
MathSciNet: MR1762909
Digital Object Identifier: 10.1214/aos/1016120370

Primary: 62F05 , 62G10 , 62G20

Keywords: Anderson–Darling test , Bahadur efficiency , Cramér –von Mises test , intermediate or Kallenberg efficiency , Pitman efficiency , Shortcoming

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • February 2000
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