## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 3 (1976), 597-606.

### Asymptotic Expansion and a Local Limit Theorem for a Function of the Kendall Rank Correlation Coefficient

#### Abstract

In the present paper, an integer-valued version $(T_N)$ of the Kendall rank correlation coefficient is considered. Under the hypothesis of independence, a local limit theorem with the Edgeworth expansion for $T_N$ is proved and an asymptotic expansion of the distribution function of $T_N$ is derived.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 3 (1976), 597-606.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343465

**Digital Object Identifier**

doi:10.1214/aos/1176343465

**Mathematical Reviews number (MathSciNet)**

MR405670

**Zentralblatt MATH identifier**

0336.62033

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 60E05: Distributions: general theory 60F05: Central limit and other weak theorems

**Keywords**

Kendall rank correlation coefficient characteristic function Esseen inequality asymptotic expansion

#### Citation

Praskova-Vizkova, Zuzana. Asymptotic Expansion and a Local Limit Theorem for a Function of the Kendall Rank Correlation Coefficient. Ann. Statist. 4 (1976), no. 3, 597--606. doi:10.1214/aos/1176343465. https://projecteuclid.org/euclid.aos/1176343465