关于中心极限定理收敛速度的一个不等式(英文)

On aninequality of convergence rate for the central limit theorem

利用已知的不等式,通过构造一类特殊的函数,推广了某个经典结果:设{Xn:n≥1}是零均值独立r.v.序列,若∈Θ,使得E(X2i(Xi))<∞,其中Θ={(x):(x)是非负偶函数;且(x)、x/(x)在(0,+∞)上单调不减},则存在正常数K,使得supxFn(x)-Φ(x)≤B2n(KBn)∑i=n1E(x2i(xi)).使之及某些已知结果成为本文的特例.

Using the given inequalities, we get a more generalized inequality of the central limit theorem（CLT）, by constructing a special function. As corollaries, a class of knowledge already known are the particular eases of the result in this paper.