An estimate of the remainder of a limit theorem

作者：He, Jianjun^*

来源：Statistics & Probability Letters, 2012, 82(3): 478-487.

DOI：10.1016/j.spl.2011.11.009

• The rate of approximation
• I.i.d. random variable
• Complete convergence

Let {X, X-n, n >= 1} be a sequence of i.i.d. random variables with zero mean and finite variance. Set S-n = Sigma(n)(k=1) X-k, EX2 = sigma(2) > 0, lambda(alpha)(epsilon) = Sigma(infinity)(n=1), P(|S-n| >= n(1/2+alpha) epsilon), 0 < alpha < 1. In this paper, we discuss the rate of the approximation of sigma (1/alpha) C-alpha by epsilon(1/alpha)lambda(alpha) under suitable conditions, and extend the results of Klesov (1994), and He and Xie (in press), where C-alpha = pi(-1/2)2(1/2 alpha) Gamma(1/2 + 1/2 alpha).

• 出版日期2012-3
• 单位中国计量大学