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March, 1977 Note on Conditions for Weak Convergence of Von Mises' Differentiable Statistical Functions
N. Bonner, H.-P. Kirschner
Ann. Statist. 5(2): 405-407 (March, 1977). DOI: 10.1214/aos/1176343807

Abstract

In establishing weak convergence of von Mises' differentiable statistical functions to a normal distribution usually square integrability conditions with respect to the underlying kernel function are assumed. It is shown that these conditions can be weakened by assuming integrability of the von Mises' functional itself. In addition it is pointed out that in nontrivial cases the conditions of square integrability of the kernel do not hold whereas weak convergence of the von Mises' functional can still be proved.

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N. Bonner. H.-P. Kirschner. "Note on Conditions for Weak Convergence of Von Mises' Differentiable Statistical Functions." Ann. Statist. 5 (2) 405 - 407, March, 1977. https://doi.org/10.1214/aos/1176343807

Information

Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0358.62018
MathSciNet: MR428545
Digital Object Identifier: 10.1214/aos/1176343807

Subjects:
Primary: 62E20
Secondary: 62E15

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 2 • March, 1977
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