The Annals of Probability

Inequalities for Conditioned Normal Approximations

D. Landers and L. Rogge

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Abstract

Let $X_n$ be a sequence of i.i.d. random variables with mean 0 and variance 1. Let $S_n^\ast = n^{-\frac{1}{2}} \sum^n_{\nu=1} X_\nu$. We investigate in this paper the convergence order in conditioned central limit theorems, that is, the convergence order of $\sup_{t\in\mathbb{R}}|P(S_n^\ast < t|B) - \phi(t)|$.

Article information

Source
Ann. Probab., Volume 5, Number 4 (1977), 595-600.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995769

Digital Object Identifier
doi:10.1214/aop/1176995769

Mathematical Reviews number (MathSciNet)
MR440668

Zentralblatt MATH identifier
0368.60027

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J15

Keywords
Conditional approximation order of convergence

Citation

Landers, D.; Rogge, L. Inequalities for Conditioned Normal Approximations. Ann. Probab. 5 (1977), no. 4, 595--600. doi:10.1214/aop/1176995769. https://projecteuclid.org/euclid.aop/1176995769


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