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August, 1977 Inequalities for Conditioned Normal Approximations
D. Landers, L. Rogge
Ann. Probab. 5(4): 595-600 (August, 1977). DOI: 10.1214/aop/1176995769

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 $\sup_{t\in\mathbb{R}}|P(S_n^\ast < t|B) - \phi(t)|$.

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D. Landers. L. Rogge. "Inequalities for Conditioned Normal Approximations." Ann. Probab. 5 (4) 595 - 600, August, 1977. https://doi.org/10.1214/aop/1176995769

Information

Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0368.60027
MathSciNet: MR440668
Digital Object Identifier: 10.1214/aop/1176995769

Subjects:
Primary: 60F05
Secondary: 60J15

Keywords: Conditional approximation , order of convergence

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 4 • August, 1977
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