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October, 1986 Limit Theorems for a Triangular Scheme of $U$-Statistics with Applications to Inter-Point Distances
S. Rao Jammalamadaka, Svante Janson
Ann. Probab. 14(4): 1347-1358 (October, 1986). DOI: 10.1214/aop/1176992375

Abstract

The asymptotic distribution of a "triangular" scheme of $U$-statistics is studied. Two limit theorems, applicable in different situations, are given. One theorem yields convergence to a normal distribution; the other includes Poisson limits and other limit laws. Applications to statistics based on small interpoint distances in a sample are given.

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S. Rao Jammalamadaka. Svante Janson. "Limit Theorems for a Triangular Scheme of $U$-Statistics with Applications to Inter-Point Distances." Ann. Probab. 14 (4) 1347 - 1358, October, 1986. https://doi.org/10.1214/aop/1176992375

Information

Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0604.60023
MathSciNet: MR866355
Digital Object Identifier: 10.1214/aop/1176992375

Subjects:
Primary: 60F05
Secondary: 60E07 , 62E20

Keywords: $U$-statistics , Infinitely divisible distributions , inter-point distances , limit laws , multigraph , triangular scheme

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • October, 1986
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