U-统计量的非一致性界限

设U_n为U-统计量,其核具有三阶有限矩,又本文建立了下列F_n(x)向标准正态分布Φ(x)收敛的非一致性收敛速度估计其中C为与n、x都无关的常数。     

Student U-统计量的Berry-Esseen界

在 2 +δ阶矩存在的条件下 ,建立了StudentU 统计量的Berry Esseen界O(n-δ/2 )     

有限总体U-统计量的Berry-Esseen界限

设AN为标有实数指标的N个球的一个总体,从中无放回地随机抽取n个球,其指标分别记为x₁,…,x_n.设φN(x,y)为关于x,y对称的二元Borel可测函数,记θ_N=E_φN(x₁,x₂),g(x₁)=E(φN(x₁,x₂)|x₁),σ_g²=Var(g(x₁)).本文证明了:若存在固定常数λ₁,λ₂,使0<λ₁≤n/NP_N≤λ_2<1,则存在仅与λ₁,λ₂有关的绝对常数C,使其中Φ(x)标准正态分布函数。     

关于U-统计量的非一致性收敛速度

研究了高阶矩条件下,U-统计量的非一致性收敛速度,给出了一系列平行于独立和的理想结果.     

关于U-统计量的Berry-Esseen不等式的推广

设{X_n}是独立同分布随机变量序列,共同的分布函数为F(x)。φ(x,y)是二元对     

U-统计量的分布的非一致性收敛速度

Callaert和Janssen在只假定核的三阶矩有限的条件下,得到了U-统计量的分布的最佳一致性收敛速度O(n^-1/2)。本文在同样条件下,得到了理想的非一致性收敛速度O(n^-1/2(1+|x|)^-3)。     

U-统计量的分布的非一致性收敛速度

设{X_n}为一串iid.随机变量,h(x,y)为两个变元x,y的对称函数,则称 U_n=(?)~(-1) sum from (i≤i相似文献   

关于Von Mises统计量Berry-Esseen定理的一点注记

Let V_n be a von Mises Statistice with kernel φ(x₁,x₂,… ,x_m).     

U-统计量的几乎处处中心极限定理

本文得到了U-统计量的几乎处处中心极限定理(ASCLT).在EX1=0,EX21=1下,Berkes等[7]在一定条件下获得了i.i.d.随机变量序列部分和的函数型ASCLT,本文在同样的条件下取得了类似的结果.     

U-统计量的几乎处处中心极限定理

本文得到了U-统计量的几乎处处中心极限定理(ASCLT).在EX1=0,EX2=1下,Berkes等[7]在一定条件下获得了i.i.d.随机变量序列部分和的函数型ASCLT,本文在同样的条件下取得了类似的结果     

A Non-Uniform Estimate in the Central Limit Theorem for Sequences of Strongly Additive Functions

The value distribution of a normalised sequence of strongly additive arithmetic functions

An Inductive Proof of the Berry-Esseen Theorem for Character Ratios

Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions. Received March 11, 2005     

The Berry-Esseen bound for studentized U-statistics

We establish the Berry-Esseen bound O(n/2) for a studentized U-statistic under the assumption of existence of the (2+)-th moment.     

The Berry-Esseen bound for character ratios

Let be a partition of chosen from the Plancherel measure of the symmetric group , let be the irreducible character of the symmetric group parameterized by evaluated on the transposition , and let be the dimension of the irreducible representation parameterized by . Fulman recently obtained the convergence rate of for any in the central limit theorem for character ratios by developing a connection between martingale and character ratios, and he conjectures that the correct speed is . In this paper we confirm the conjecture via a refinement of Stein's method for exchangeable pairs.

     

半参数回归模型中误差方差估计的Berry-Esseen界

综合最小二乘法和局部线性光滑法给出了半参数回归模型中误差方差的估计量σ_n~2,在适当的条件下,证明了σ_n~2的Berry-Esseen界可达到O(n-1／2).     

The Berry-Esseen theorem for functions of uniform spacings

Summary A Berry-Esseen bound of order is established for suitably normalized sums of nonlinear measurable functions of uniform spacings under the natural moment assumptions.Some of this study was carried out at the Mathematical Centre, Amsterdam, and some of it when the second author was a member of the Mathematical Sciences Research Institute, Berkeley     

The Berry-Esseen theorem for functionals of discrete Markov chains

Summary The error bound O(1/n) is derived in the central limit theorem for partial sums where _j is a recurrent discrete Markov chain and f is a real valued function on the state space. In particular it is shown that for bounded f and starting distribution dominated by some multiple of the stationary one, it is sufficient for the chain to have recurrence times with third moments on order to get this bound.     

基于Stein方法的均衡分布的Berry-Esseen界

受Shao和Su(2006)的启发,获得了均衡分布的Berry-Esseen界,定理的证明基于Stein方法.