[1]阮宏顺.一类线性过程中的分布函数的收敛速度[J].常州大学学报(自然科学版),2003,(01):47-49.
　RUAN Hong -shun.Rate of Convergence for the Distribution Function of a Broad Class of Linear Processes[J].Journal of Changzhou University(Natural Science Edition),2003,(01):47-49.
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一类线性过程中的分布函数的收敛速度()
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常州大学学报(自然科学版)[ISSN:2095-0411/CN:32-1822/N]

卷:
期数:
2003年01期
页码:
47-49
栏目:
出版日期:
2003-03-25

文章信息/Info

Title:
Rate of Convergence for the Distribution Function of a Broad Class of Linear Processes
作者:
阮宏顺
江苏工业学院信息科学系, 江苏 常州 213016
Author(s):
RUAN Hong -shun
Department of Information and Science , Jiang su Polytechnic University , Changzhou 213016 , China
关键词:
线性过程; 分布函数; 收敛速度
Keywords:
linear process; dist ribution function ; rate of convergence
分类号:
O 211
文献标志码:
A
摘要:
考虑线性过程:X (n) = Σ ∞ i =0 δ(i) Z (n -i), 在如下条件下:①Z (n) 为i.i.d.r.v′s , 且E Z (n) <∞;② Z (n) 的分布函数F 具有有界密度;③参数δ(i) 满足 δ(i)
Abstract:
This paper dealt with uniform rate of convergence for a broad class of stationary linear processes :X (n) =Σ ∞ i =0 δ(i)Z (n -i)wasconsidered under the condit ion that ①Z (n)(n =1 , 2 , …)is i.i.d.r.v′s w ith a finite first absolute moment , ②the dist ribution functionF of X (n )bounded density , and ③the parameters δ(i)were bounded in absolute value by some function g which satisfies Σ ∞ i =1 ig (i) <∞.It was proved that the distribution function F Vm (x )converged to F (x ), uniformly in x , at a rate O((g (h (m)))1/2)a.s.w hich wasfaster than that of [ 1] on the same condition .

参考文献/References:

[1] Hesses C H .Rat es of Convergence f or the Empirical Dist ribution Function and the Empirical C haract eristi c Function of a Broad C lass of Linear Processes [J] .J Mult Anal , 1990 , 35 :186 -220.
[2] C hung K L .An Estimat e Concerning the Kolmogolov Limi t Di st ribut ion [J] .T rans Amer Math Soc, 1949 , 67 :36 -50 .
[3] Smirnov N V .Approximat e Law s of Distribution Random Varaiabies from Empirical Data [J] .Uspeh ki Mat Nauk , 1944 , 10 : 179 -206 .
[4] 阮宏顺, 许波.线性过程中核估计的强一致相合性[J] .江 苏石油化工学院学报, 1998 , 10 (1):38 -40.

相似文献/References:

[1]阮宏顺.一类线性过程中的经验分布函数的收敛速度[J].常州大学学报(自然科学版),2005,(03):34.
　RUAN Hong -shun.Rate of Convergence for the Empirical Distribution Function of a Broad Class of Linear Processes[J].Journal of Changzhou University(Natural Science Edition),2005,(01):34.

备注/Memo

备注/Memo:
基金项目:江苏省高校自然科学研究项目(02KJD110001);江苏工业学院科技基金资助 作者简介:阮宏顺(1955 -), 男, 安徽安庆人, 副教授, 硕士, 主要从事概率极限理论研究。
更新日期/Last Update: 2003-03-25