## The Annals of Probability

### Inequalities for Conditioned Normal Approximations

#### 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

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