The Annals of Statistics

Note on Conditions for Weak Convergence of Von Mises' Differentiable Statistical Functions

N. Bonner and H.-P. Kirschner

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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.

Article information

Source
Ann. Statist., Volume 5, Number 2 (1977), 405-407.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343807

Digital Object Identifier
doi:10.1214/aos/1176343807

Mathematical Reviews number (MathSciNet)
MR428545

Zentralblatt MATH identifier
0358.62018

JSTOR
links.jstor.org

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

Keywords
Von Mises' differentiable statistical functions $U$-statistics weak convergence

Citation

Bonner, N.; Kirschner, H.-P. Note on Conditions for Weak Convergence of Von Mises' Differentiable Statistical Functions. Ann. Statist. 5 (1977), no. 2, 405--407. doi:10.1214/aos/1176343807. https://projecteuclid.org/euclid.aos/1176343807


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