The Annals of Statistics

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

C. P. Shapiro and Lawrence Hubert

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62E15: Exact distribution theory

Keywords
Nonparametric permutation distribution clustering statistics

Citation

Shapiro, C. P.; Hubert, Lawrence. Asymptotic Normality of Permutation Statistics Derived from Weighted Sums of Bivariate Functions. Ann. Statist. 7 (1979), no. 4, 788--794. doi:10.1214/aos/1176344728. https://projecteuclid.org/euclid.aos/1176344728


Export citation