### Inequalities for Conditioned Normal Approximations

D. Landers and L. Rogge
Source: Ann. Probab. Volume 5, Number 4 (1977), 595-600.

#### 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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Primary Subjects: 60F05
Secondary Subjects: 60J15
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