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October, 1975 On Errors of Normal Approximation
R. N. Bhattacharya
Ann. Probab. 3(5): 815-828 (October, 1975). DOI: 10.1214/aop/1176996268

Abstract

Let $Q_n$ be the distribution of the normalized sum of $n$ independent random vectors with values in $R^k$, and $\Phi$ the standard normal distribution in $R^k$. In this article the error $|\int f d(Q_n - \Phi)|$ is estimated (for essentially) all real-valued functions $f$ on $R^k$ which are integrable with respect to $Q_n$ when $s$th moments are finite, and for which the error may be expected to go to zero. When specialized to known examples, the (main) error bound provides precise rates of convergence.

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R. N. Bhattacharya. "On Errors of Normal Approximation." Ann. Probab. 3 (5) 815 - 828, October, 1975. https://doi.org/10.1214/aop/1176996268

Information

Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0319.60013
MathSciNet: MR467879
Digital Object Identifier: 10.1214/aop/1176996268

Subjects:
Primary: 60F05

Keywords: average oscillations , central limit theorem , Fourier transform , rates of convergence

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • October, 1975
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