## The Annals of Statistics

### Asymptotic Normality of Permutation Statistics Derived from Weighted Sums of Bivariate Functions

#### Abstract

Statistics of the form $H_n = \sum d_{ijn}h_n(X_i, X_j)$ are considered, where $X_1, X_2, \cdots$, are independent and identically distributed random variables, the diagonal terms, $d_{iin}$, are equal to zero, and $h_n(x, y)$ is a symmetric real valued function. The asymptotic normality of such statistics is proven and the result then combined with work of Jogdeo on statistics that are weighted sums of bivariate functions of ranks to find sufficient conditions for asymptotic normality of permutation statistics derived from $H_n$.

#### Article information

Source
Ann. Statist., Volume 7, Number 4 (1979), 788-794.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344728

Digital Object Identifier
doi:10.1214/aos/1176344728

Mathematical Reviews number (MathSciNet)
MR532242

Zentralblatt MATH identifier
0423.62020

JSTOR