共查询到20条相似文献,搜索用时 0 毫秒
1.
LIN Zhengyan 《中国科学A辑(英文版)》2000,43(11):1154-1163
We establish the Berry-Esseen bound O(n/2) for a studentized U-statistic under the assumption of existence of the (2+)-th moment. 相似文献
2.
Jason Fulman 《Transactions of the American Mathematical Society》2008,360(7):3687-3730
Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is obtained for a central limit theorem of Kerov on the spectrum of the Cayley graph of the symmetric group generated by -cycles. Other main examples include an error term for a central limit theorem of Ivanov on character ratios of random projective representations of the symmetric group, and a new central limit theorem for the spectrum of certain random walks on perfect matchings. The results are obtained with very little information: a character formula for a single representation close to the trivial representation and estimates on two step transition probabilities of a random walk. The limit theorems stated in this paper are for normal approximation, but many of the tools developed are applicable for arbitrary distributional approximation.
3.
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. 相似文献
4.
Guang-hui Cai 《高校应用数学学报(英文版)》2012,27(4):455-461
In this paper, we obtain the Berry-Esseen bound for identically distributed random variables by Stein method. The results obtained generalize the results of Shao and Su (2006) and Stein (1986). 相似文献
5.
Jason Fulman 《Transactions of the American Mathematical Society》2005,357(2):555-570
We initiate a Stein's method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov's central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the proof gives an error term. The construction of an exchangeable pair needed for applying Stein's method arises from the theory of harmonic functions on Bratelli diagrams. We also find the spectrum of the Markov chain on partitions underlying the construction of the exchangeable pair. This yields an intriguing method for studying the asymptotic decomposition of tensor powers of some representations of the symmetric group.
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7.
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). 相似文献
8.
Jason Fulman 《Transactions of the American Mathematical Society》2006,358(10):4533-4552
Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burnside and Brauer on the decomposition of tensor products.
9.
Xiaojing Xiang 《Annals of the Institute of Statistical Mathematics》1995,47(2):237-251
A Berry-Esseen bound is established for the kernel quantile estimator under various conditions. The results improve an earlier result of Falk (1985,Ann. Statist.,13, 428–433) and rely on the local smoothness of the quantile function. This new Berry-Esseen bound is applied to studying the deficiency of the sample quantile estimator with respect to the kernel quantile estimator. A new result is obtained which is an extension of that in Falk (1985). 相似文献
10.
Using wavelet smoothing and least-squares methods,we investigate a heteroscedastic partly linear errors-in-variables (EV)model with $\alpha$-mixing random errors. The wavelet estimators of the parametric parts and nonparametric parts are given, and Berry-Esseen bounds of wavelet estimators are obtained under general conditions. 相似文献
11.
Guan Zhong 《东北数学》1994,(3)
ABerry-EsseenBoundfork-sampleSymmetricStatisticsGuanZhong(关忠)(DepartmentofMathematics,HarbinInstituteofTechnology,Harbin,1500... 相似文献
12.
We construct a precise Berry-Esseen bound for the least squares error variance estimators of regression parameters. Our bound
depends explicitly on the sequence of design variables and is of the order O(N
−1/2) if this sequence is “regular” enough.
Supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 1–8, January–March, 1999. 相似文献
13.
考虑独立同分布的随机环境中带移民的上临界分枝过程(Zn).应用(Zn)与随机环境中不带移民分枝过程的联系,以及与相应随机游动的联系,在一些适当的矩条件下,本文证明关于log Zn的中心极限定理的Berry-Esseen界. 相似文献
14.
Khac Viet Nguyen 《Proceedings of the American Mathematical Society》1999,127(11):3125-3130
We prove a complex function field analogue of Szpiro's conjecture for hyperelliptic curves and some applications. The cases of function fields of positive characteristic and number fields are discussed briefly.
15.
This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier's theorem concerning the induction of Whittaker models is proved for Bessel models which are minimal in a suitable sense. The holomorphicity in the induction parameter of the Bessel functional is established. Local coefficients are defined for each irreducible supercuspidal representation which carries a Bessel functional and also for a certain component of each representation parabolically induced from such a supercuspidal. The local coefficients are related to the Plancherel measures, and their zeroes are shown to be among the poles of the standard intertwining operators. 相似文献
16.
设$(Z_{n})_{n\geq 0}$为一个在独立同分布随机环境下的上临界分支过程。我们对$(Z_{n})_{n\geq 0}$的Wasserstein-1距离证得一个最优的收敛速度,该结果补充了Grama等[Stochastic Process. Appl., 2017, 127(4): 1255--1281]的结论. 此外, 本文也给出了指数非一致性的 Berry-Esseen 界. 最后本文还讨论了通过运用主要结果而得到的关键参数和人口数量$Z_n$的置信区间估计. 相似文献
17.
Smarandache函数的一个下界估计 总被引:1,自引:0,他引:1
温田丁 《纯粹数学与应用数学》2010,26(3):413-416
利用初等及组合方法研究Smarandache函数在梅森尼素数上的下界估计问题,给出了Smarandache函数在这一数列上的一个较强的下界估计,从而改进了相关文献的一个结果. 相似文献
18.
Let be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate deviations and Berry-Esseen bounds for log( ) uniformly in ,which extend the corresponding results by I. Grama, Q. Liu, and M. Miqueu [Stochastic Process. Appl., 2017, 127: 1255–1281] established for . The extension is interesting in theory, and is motivated by applications. A new method is developed for the proofs; some conditions of Grama et al. are relaxed in our present setting. An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log( ) and n. 相似文献
19.
§ 1 IntroductionConsiderthefollowingnonlinearoptimizationproblem :minimizef(x)subjecttoC(x) =0 , a≤x≤b ,( 1 .1 )wheref(x) :Rn→R ,C(x) =(c1(x) ,c2 (x) ,...,cm(x) ) T:Rn→Rm aretwicecontinuouslydifferentiable,m≤n ,a ,b∈Rn.Trustregionalgorithmsareveryeffectiveforsolvingnonlinearoptimi… 相似文献
20.
关于Smarandache函数的一个新的下界估计 总被引:3,自引:1,他引:3
利用初等方法研究Smarandache函数在某些特殊值上的下界估计,给出了Smarandache函数在某些特殊值上的一个较强的下界估计,证明了估计式S(2p+1)≥6p+1,其中P≥7为任意素数. 相似文献