## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 40, Number 6 (1969), 1992-2017.

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

Vaclav Dupac and Jaroslav Hajek

#### Abstract

This is a straightforward continuation of Hajek (1968). We provide a further extension of the Chernoff-Savage (1958) limit theorem. The requirements concerning the scores-generating function are relaxed to a minimum: we assume that this function is a difference of two non-decreasing and square integrable functions. Thus, in contradistinction to Hajek (1968), we dropped the assumption of absolute continuity. The main results are accumulated in Section 2 without proofs. The proofs are given in Sections 4 through 7. Section 3 contains auxiliary results.

#### Article information

**Source**

Ann. Math. Statist., Volume 40, Number 6 (1969), 1992-2017.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697281

**Digital Object Identifier**

doi:10.1214/aoms/1177697281

**Mathematical Reviews number (MathSciNet)**

MR253487

**Zentralblatt MATH identifier**

0193.17401

**JSTOR**

links.jstor.org

#### Citation

Dupac, Vaclav; Hajek, Jaroslav. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II. Ann. Math. Statist. 40 (1969), no. 6, 1992--2017. doi:10.1214/aoms/1177697281. https://projecteuclid.org/euclid.aoms/1177697281