共查询到19条相似文献,搜索用时 46 毫秒
1.
证明了Burr分布和Frechet分布的记录值序列的部分和是渐进对数正态的,从而解决了[2]中的一个悬而未决的问题。 相似文献
2.
不同分布NA列加权和的强极限定理及其在线性模型中的应用 总被引:11,自引:0,他引:11
本文讨论了不同分布NA列Stout型加权和的完全收敛性和强稳定性,推广并改进了Stout关于iid列的相应结果,从而将赵林城关于独立误差的方差估计的强收敛速度的理想结果推广到NA误差的场合。 相似文献
3.
证明了 Burr分布和 Frechét分布的记录值序列的部分和是渐进对数正态的 ,从而解决了文[2 ]中的一个悬而未决的问题 相似文献
4.
5.
李云霞 《数学物理学报(A辑)》2006,26(5):675-687
该文主要讨论的是滑线性过程 $X_k=\sum\limits_{i=-\infty}^\infty a_{i+k}\varepsilon_i$,其中 $\{\varepsilon_i; -\infty$\varphi$ -混合或负相伴随机变量序列,$\{a_i;-\inftyp$, 若 $E|\varepsilon_1|^r<\infty$$\lim_{\epsilon\searrow 0}\epsilon^{2(r-p)/(2-p)}\sum\limits_{n=1}^\infty n^{r/p-2}P\{|S_n|\geq \epsilonn^{1/p}\}=\frac{p}{r-p}E|Z|^{2(r-p)/(2-p)},$ 其中 $Z$ 是服从均值为零,方差为 $\tau^2=\sigma^2\cdot(\sum\limits_{i=-\infty}^\infty a_i)^2$的正态分布. 相似文献
6.
7.
8.
考虑线性回归模型y=xTβ+e1其中误差e是函数系数自回归(FCA)过程.本文研究该模型未知参数的Huber-Dutter估计的渐近性质,在合理的条件下,证明了这些估计量以n-(1/2)速度渐近于正态分布. 相似文献
9.
强混合样本下回归加权估计的一致渐近正态性 总被引:5,自引:0,他引:5
在强混合样本下,讨论固定设计回归模型的加权函数估计的一致渐近正态性,给出一致渐近正态性的收敛速度,这个速度接近n-1/6. 相似文献
10.
该文讨论了非平稳负(正)相依序列加权和的几乎处处中心极限定理,改进并推广了相依序列几乎处处中心极限定理的相关结果. 相似文献
11.
Asymptotic Normality for Non-linear Functionals of Non-causal Linear Processes with Summable Weights
Let
be a non-causal linear process with weights ajs satisfying certain summability conditions, and the iid sequence of innovation {i} having zero mean and finite second moment. For a large class of non-linear functional K which includes indicator functions and polynomials, the present paper develops the
central limit theorem for the partial sums
相似文献
12.
Shuyuan He 《Journal of multivariate analysis》1996,58(2):182-188
We consider a stationary time series {Xt} given byXt=∑∞k=−∞ ψkZt−k, where {Zt} is a strictly stationary martingale difference white noise. Under assumptions that the spectral densityf(λ) of {Xt} is squared integrable andmτ ∑|k|?m ψ2k→0 for someτ>1/2, the asymptotic normality of the sample autocorrelations is shown. For a stationary long memoryARIMA(p, d, q) sequence, the conditionmτ ∑|k|?m ψ2k→0 for someτ>1/2 is equivalent to the squared integrability off(λ). This result extends Theorem 4.2 of Cavazos-Cadena [5], which were derived under the conditionm ∑|k|?m ψ2k→0. 相似文献
13.
Guangyu Zou & Yong Zhang 《数学研究通讯:英文版》2012,28(4):359-366
In this paper, we prove an almost sure central limit theorem for weighted
sums of mixing sequences of random variables without stationary assumptions. We no
longer restrict to logarithmic averages, but allow rather arbitrary weight sequences.
This extends the earlier work on mixing random variables. 相似文献
14.
设{Xni,un≤i≤vn,n≥1}与{ani,un≤i≤vn,n≥1}分别为一个随机阵列和一个常数阵列.本文首先引入了随机阵列{Xni,un≤i≤vn,n≥1}关于常数阵列{ani,un≤i≤vn,n≥1}剩余h-可积的概念,它是弱于h-可积,Cesaroα-可积等其它相关可积的定义.然后在这一可积的定义和适当的条件下,我们研究了相依随机序列加权和的强收敛性和平均收敛性,推广并改进了相关文献已有结果. 相似文献
15.
FangWANG ShiHongCHENG 《数学学报(英文版)》2004,20(5):869-878
We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d, random variables with E X1 = 0, EX1^2 = 1. 相似文献
16.
Florence Merlevède Magda Peligrad Sergey Utev 《Journal of Theoretical Probability》1997,10(3):681-693
In this paper we study the behavior of sums of a linear process
associated to a strictly stationary sequence
with values in a real separable Hilbert space and
are linear operators from H to H. One of the results is that
satisfies the CLT provided
are i.i.d. centered having finite second moments and
. We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables
under minimal conditions. 相似文献
17.
Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if
the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in
our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter
and the discrete parameter cases. The proof is based on a new central limit theorem for α-mixing random fields. Simulation
results support our theorems.
Final version 29 October 2004 相似文献
18.
We investigate the joint weak convergence (f.d.d. and functional) of the vector-valued process (U
n
(1)
(τ), U
n
(2)
(τ)) for τ ∈ [0, 1], where
and
are normalized partial-sum processes separated by a large lag m, m/n → ∞, and (X
t
, t ∈ ℤ) is a stationary moving-average process with i.i.d. (or martingale-difference) innovations having finite variance. We
consider the cases where (X
t
) is a process with long memory, short memory, or negative memory. We show that, in all these cases, as n → ∞ and m/n → ∞, the bivariate partial-sum process (U
n
(1)
(τ), U
n
(2)
(τ)) tends to a bivariate fractional Brownian motion with independent components. The result is applied to prove the consistency
of certain increment-type statistics in moving-average observations.
This work supported by the joint Lithuania-French research program Gilibert.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 479–500, October–December, 2005. 相似文献
19.
设Xn, n≥1是独立同分布正的随机变量序列, E(X1)=u >0, Var(X1)=σ2, E|X1|3<∞, 记Sn==∑Nk=1Xk, 变异系数γ=σ/u.g是满足一定条件的无界可测函数, 证明了
limN→∞1/logN∑Nn=11/n g((∏nk=1Sk/n!un )1/γ√n )=∫∞0g(x)dF(x),a.s.,
其中 F(•) 是随机变量e√2ξ 的分布函数, ξ 是服从标准正态分布的随机变量. 相似文献