## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 1 (1976), 108-156.

### Asymptotic Expansions for the Power of Distribution Free Tests in the One-Sample Problem

W. Albers, P. J. Bickel, and W. R. van Zwet

#### Abstract

Asymptotic expansions are established for the power of distribution free tests in the one-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann (1970) for distribution free tests with respect to their parametric competitors and for the estimators of location associated with these tests.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 1 (1976), 108-156.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343350

**Digital Object Identifier**

doi:10.1214/aos/1176343350

**Mathematical Reviews number (MathSciNet)**

MR391373

**Zentralblatt MATH identifier**

0321.62049

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 62G20: Asymptotic properties 60F05: Central limit and other weak theorems

**Keywords**

Distribution free tests linear rank tests permutation tests power contiguous alternatives Edgeworth expansions deficiency

#### Citation

Albers, W.; Bickel, P. J.; van Zwet, W. R. Asymptotic Expansions for the Power of Distribution Free Tests in the One-Sample Problem. Ann. Statist. 4 (1976), no. 1, 108--156. doi:10.1214/aos/1176343350. https://projecteuclid.org/euclid.aos/1176343350

#### Corrections

- See Correction: W. Albers, P. J. Bickel, W. R. van Zwet. Note: Correction to "Asymptotic Expansions for the Power of Distributionfree Tests in the One-Sample Problem". Ann. Statist., Volume 6, Number 5 (1978), 1170--1171.Project Euclid: euclid.aos/1176344321