共查询到20条相似文献,搜索用时 15 毫秒
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Tian-xiao Pang Li-xin Zhang Jian-feng Wang 《Journal of Mathematical Analysis and Applications》2008,340(2):1249-1262
Let X,X1,X2,… be i.i.d. nondegenerate random variables with zero means, and . We investigate the precise asymptotics in the law of the iterated logarithm for self-normalized sums, Sn/Vn, also for the maximum of self-normalized sums, max1kn|Sk|/Vn, when X belongs to the domain of attraction of the normal law. 相似文献
3.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1987,39(1):25-36
Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in
the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically
compared up to the second order, i.e. the ordern
−1/2 with the asymptotic expansions of their distributions.
University of Electro-communications 相似文献
4.
Terence Chan 《Journal of Theoretical Probability》1995,8(3):643-667
For 0<<1, let
. The questions addressed in this paper are motivated by a result due to Strassen: almost surely, lim sup
t
U
((t))=1–exp{–4(–1)–1}. We show that Strassen's result is closely related to a large deviations principle for the family of random variablesU
(t), t>0. Also, when =1,U
(t)0 almost surely and we obtain some bounds on the rate of convergence. Finally, we prove an analogous limit theorem for discounted averages of the form
as 0, whereD is a suitable discount function. These results also hold for symmetric random walks. 相似文献
5.
Let be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X2)=1, and set , n?1. This paper studies the precise asymptotics in the law of the iterated logarithm. For example, using a result on convergence rates for probabilities of moderate deviations for obtained by Li et al. [Internat. J. Math. Math. Sci. 15 (1992) 481-497], we prove that, for every b∈(−1/2,1],
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设X,X_1,X_2,…为零均值、非退化、吸引域为正态吸引场的独立同分布随机变量序列,记S_n=■X_j,M_n=■|S_k|,V_n~2=■X_j~2,n≥1.证明了当b>-1时,■δ~(-2(b 1))■(log log n)~P/(n log n)P(Mn/V_n≤ε~(π~2)/(8lgo log n)~(1/2)) =4/πГ(b 1)■~(-1)~k/(2k 1)~(2b 3). 相似文献
7.
This paper achieves a general law of precise asymptotics for the counting process of record times of i.i.d. absolutely continuous random variables. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results in Stochastic Process. Appl. 101 (2002) 233-239. 相似文献
8.
设{xn,m≥1}是独立同分布随机变量序列,EX1=0,EX12=1.设Tn= Tn(X1,…,Xn)是随机函数且Tn=Sn Rn.本文证明在E|Rn|2∨r<∞或E|Rn|<∞下,对随机函数Tn成立着Baum-Katz强大数律和重对数律的精确极限性质的一般结果.由此作为推论,对U-统计量,Von-Mises统计量,线性过程,移动平均过程,线性模型中误差方差估计和功率和等在适当矩条件下均可写出Baum-Katz强大数律和重对数律的精确极限性质. 相似文献
9.
The problem of estimation of an interest parameter in the presence of a nuisance parameter, which is either location or scale, is studied. Two estimators are considered: the usual maximum likelihood estimator and the estimator based on maximization of the integrated likelihood function. The estimators are compared, asymptotically, with respect to the bias and with respect to the mean squared error. The examples are given. 相似文献
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We establish the law of the iterated logarithm for the product limit estimator, when the data are subject to double censoring. This investigation extends the results available for the model for singly censored data. 相似文献
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This paper obtains functional modulus of continuity and Strassen's functional LIL of the infinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exact modulus of continuity and LIL of this process respectively. 相似文献
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A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION 总被引:1,自引:0,他引:1
In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained. 相似文献
13.
In this paper, we consider the kernel-type estimator of the quantile function based on the kernel smoother under a censored dependent model. The Bahadur-type representation of the kernel smooth estimator is established, and from the Bahadur representation we can show that this estimator is strongly consistent. 相似文献
14.
Katusi Fukuyama 《Acta Mathematica Hungarica》2002,97(3):257-264
Takahashi [15] gave a concrete upper bound estimate of the law of the iterated logarithm for ∑ f(n
k
x). We extend this result and prove the best possibility of this bound.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
Summary The problem to estimate a common parameter for the pooled sample from the uniform distributions is discussed in the presence
of nuisance parameters. The maximum likelihood estimator (MLE) and others are compared and it is shown that the MLE based
on the pooled sample is not (asymptotically) efficient. 相似文献
16.
《随机分析与应用》2013,31(1):181-203
Abstract We consider a sequence (Z n ) n≥1 defined by a general multivariate stochastic approximation algorithm and assume that (Z n ) converges to a solution z* almost surely. We establish the compact law of the iterated logarithm for Z n by proving that, with probability one, the limit set of the sequence (Z n ? z*) suitably normalized is an ellipsoid. We also give the law of the iterated logarithm for the l p norms, p ∈ [1, ∞], of (Z n ? z*). 相似文献
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关于ρ-混合序列对数律的收敛速度 总被引:1,自引:0,他引:1
本文研究了ρ-混合序列对数律的收敛速度,在较弱的矩条件下得到了与独立同分布实随机变量类似的结果,并获得了ρ-混合序列满意对数律的一个充分性结果;讨论了ρ-混合序列重对数律的收敛速度的问题,得到了一个重对数律的充分性条件。 相似文献
18.
本文研究一类生物复制网络模型最大度数的极限行为.利用鞅技术,讨论最大度数的大数定律和中心极限定理,进一步,证明最大度数满足重对数律,本文得到的结果在某种意义下能为生物学家研究生物内部机制提供理论依据. 相似文献
19.
An upper bound estimate in the law of the iterated logarithm for Σf(n
k ω) where nk+1∫nk≧ 1 + ck
-α (α≧0) is investigated. In the case α<1/2, an upper bound had been given by Takahashi [15], and the sharpness of the bound
was proved in our previous paper [8]. In this paper it is proved that the upper bound is still valid in case α≧1/2 if some
additional condition on {n
k} is assumed. As an application, the law of the iterated logarithm is proved when {n
k} is the arrangement in increasing order of the set B(τ)={1
i
1...qτ
i
τ|i1,...,iτ∈N
0}, where τ≧ 2, N
0=NU{0}, and q
1,...,q
τ are integers greater than 1 and relatively prime to each others.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献