Rates of Convergence in Normal Approximation Under Moment Conditions Via New Bounds on Solutions of the Stein Equation
Rates of Convergence in Normal Approximation Under Moment Conditions Via New Bounds on Solutions of the Stein Equation
复制标题
通过斯坦因方程解的新界在矩条件下正规逼近的收敛率
DOI：
10.1007/s10959-014-0562-z
复制
发表时间：
2013
影响因子：
0.8
通讯作者：
Robert E. Gaunt
中科院分区：
文献类型：
--
作者：
Robert E. Gaunt
得到了正态和多元正态Stein方程解的$$k$$ k阶导数的新界。与现有文献相比，我们的一般阶限涉及的测试函数导数较少。我们应用这些边界和局部方法耦合来获得一个阶$$n^{-(p-1)/2}$$ n-(p-1)/2边界，对于光滑测试函数，当这些分布的第一个$$p$$ p矩一致时，独立和同分布随机变量的标准化和的分布与标准正态分布之间的距离。我们还得到了当矩序列收敛于正态矩时，分布序列收敛于正态分布的收敛速率的一个界。
New bounds for the $$k$$kth-order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature. We apply these bounds and local approach couplings to obtain an order $$n^{-(p-1)/2}$$n-(p-1)/2 bound, for smooth test functions, for the distance between the distribution of a standardised sum of independent and identically distributed random variables and the standard normal distribution when the first $$p$$p moments of these distributions agree. We also obtain a bound on the convergence rate of a sequence of distributions to the normal distribution when the moment sequence converges to normal moments.