Student t统计量中心极限定理的精确收敛速度和首项
Exact convergence rate and leading term in central limit theorem for student's t statistic
摘要：
首项在正常的近似分布的学生的t统计量是在一般的设置，唯一的假设是，抽样分布是在吸引区域的正常法律。的形式的首项示出有其起源的方式，极端的数据影响属性的学生化和。利用首项逼近给出了中心极限定理在n^{-1/2}阶的精确收敛速率，其中n表示样本量.证明了在整条实直线上一致的精确速率与在三点集上的精确速率相同。此外，确切的速率是相同的，为非学生化的总和时，后者是标准化的规模使用截断形式的方差，但当相应的截断中心常数被省略。文中还给出了收敛速度的一些表征。它表明，在某些情况下，他们的有效性一致地在整个实数线上是等价于他们的有效性只有两个对称点。
英文摘要：
The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation is used to give the exact rate of convergence in the central limit theorem up to order n^{-1/2}, where n denotes sample size. It is proved that the exact rate uniformly on the whole real line is identical to the exact rate on sets of just three points. Moreover, the exact rate is identical to that for the non-Studentized sum when the latter is normalized for scale using a truncated form of variance, but when the corresponding truncated centering constant is omitted. Examples of characterizations of convergence rates are also given. It is shown that, in some instances, their validity uniformly on the whole real line is equivalent to their validity on just two symmetric points.
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