The Annals of Probability

On Errors of Normal Approximation

R. N. Bhattacharya

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 3, Number 5 (1975), 815-828.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996268

Digital Object Identifier
doi:10.1214/aop/1176996268

Mathematical Reviews number (MathSciNet)
MR467879

Zentralblatt MATH identifier
0319.60013

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Central limit theorem rates of convergence average oscillations Fourier transform

Citation

Bhattacharya, R. N. On Errors of Normal Approximation. Ann. Probab. 3 (1975), no. 5, 815--828. doi:10.1214/aop/1176996268. https://projecteuclid.org/euclid.aop/1176996268


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