## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 39, Number 2 (1968), 325-346.

### Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives

#### Abstract

Results of Chernoff-Savage (1958) and Govindarajulu-LeCam-Raghavachari (1966) are extended from the two-sample case to the general regression case and, simultaneously, the conditions on the scores-generating function are relaxed. The main results are stated in Section 2 and their proofs are given in Section 5. Sections 3 and 4 contain auxiliary propositions, on which the methods of the present paper are based. Section 6 includes a counterexample, showing that the theorem cannot be extended to discontinuous scores-generating functions.

#### Article information

**Source**

Ann. Math. Statist., Volume 39, Number 2 (1968), 325-346.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177698394

**Digital Object Identifier**

doi:10.1214/aoms/1177698394

**Mathematical Reviews number (MathSciNet)**

MR222988

**Zentralblatt MATH identifier**

0187.16401

**JSTOR**

links.jstor.org

#### Citation

Hajek, Jaroslav. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives. Ann. Math. Statist. 39 (1968), no. 2, 325--346. doi:10.1214/aoms/1177698394. https://projecteuclid.org/euclid.aoms/1177698394