A Berry--Esseen theorem for weakly negatively dependent random variables and its applications

Authors: Wang, Jianfeng; Zhang, Lixin

Source: Acta Mathematica Hungarica, Volume 110, Number 4, March 2006 , pp. 293-308(16)

Publisher: Springer

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Abstract:

We provide uniform rates of convergence in the central limit theorem for linear negative quadrant dependent (LNQD) random variables. Let ]]>]]>]]>]]>]]>\{X_{n},\allowbreak n\ge1\}$ be a LNQD sequence of random variables with $EX_{n}=0$, set $S_{n}=\sum_{j=1}^{n}X_{j}$ and $B_{n}^{2}=\Var\, (S_{n})$. We show that \begin{gather*} \sup_{x} \left|P\left(\frac{S_{n}}{B_{n}}
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