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February, 1972 Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
R. G. Miller Jr., Pranab Kumar Sen
Ann. Math. Statist. 43(1): 31-41 (February, 1972). DOI: 10.1214/aoms/1177692698


For partial cumulative sums of independent and identically distributed random variables (i.i.d.r.v.) with a finite (positive) variance, weak convergence to Brownian motion processes has been established by Donsker (1951, 1952). The result is extended here to differentiable statistical functions of von Mises (1947) and $U$-statistics of Hoeffding (1948). Along with the extension to generalized $U$-statistics, a few applications are briefly sketched.


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R. G. Miller Jr.. Pranab Kumar Sen. "Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions." Ann. Math. Statist. 43 (1) 31 - 41, February, 1972.


Published: February, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0238.62057
MathSciNet: MR300321
Digital Object Identifier: 10.1214/aoms/1177692698

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 1 • February, 1972
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