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991.
Arup Bose 《Annals of the Institute of Statistical Mathematics》1995,47(2):267-271
A simple estimate of the asymptotic dispersion matrix of theL
1 median is proposed and its rate of convergence is studied.Research supported in part by a grant of the Indian Statistical Institute. 相似文献
992.
Let Xt = Σ∞j=-∞ cjZt - j be a moving average process where {Zt} is iid with common distribution in the domain of attraction of a stable law with index , 0 < < 2. If 0 < < 2, E|Z1| < ∞ and the distribution of |Z1|and |Z1Z2| are tail equivalent then the sample correlation function of {X1} suitably normalized converges in distribution to the ratio of two dependent stable random variables with indices and /2. This is in sharp contrast to the case E|Z1| = ∞ where the limit distribution is that of the ratio of two independent stable variables. Proofs rely heavily on point process techniques. We also consider the case when the sample correlations are asymptotically normal and extend slightly the classical result. 相似文献
993.
Anscombe (1952) (also see Chung (1974)) has developed a central limit theoremof random sums of independent and identically distributed random variables. Applicability of this theorem in practice, however, is limited since the normalization requires random factors. In this paper we establish sufficient conditions under which the central limit theorem holds when such random factors are replaced by the underlying asymptotic mean and standard ddeviation. An application of this result in the context of shock models is also given. 相似文献
994.
A central limit theorem is obtained for orthogonally invariant random variables on
n, the space of n × n real, positive definite symmetric matrices. The derivation requires the Taylor expansion of the spherical functions for the general linear group GL(n, R). This extends from the case n = 3 a result of Terras (J. Multivariate Anal. 23 (1987), 13–36). 相似文献
995.
A field extension L / F is called excellent if, for any quadratic form over F, the anisotropic part (L)an of over L is defined over F; L / F is called universally excellent if L E / E is excellent for any field extension E / F. We study the excellence property for a generic splitting field of a central simple F-algebra. In particular, we show that it is universally excellent if and only if the Schur index of the algebra is not divisible by 4. We begin by studying the torsion in the second Chow group of products of Severi–Brauer varieties and its relationship with the relative Galois cohomology group H3(L / F) for a generic (common) splitting field L of the corresponding central simple F-algebras. 相似文献
996.
Vladimir I. Chebotarev 《Journal of Theoretical Probability》1999,12(1):13-25
In 1984, Bentkus,(2, 3) and independently,Nagaev and Chebotarev,(11) introduced somemodifications of the well-known one-dimensional Cramér conditionlim sup|t| |E
e
it| < 1 for the case of Hilbert space (denote it by H). Although many H-valued random variables satisfy these conditions, there remained open the question if these conditionshold for the random variable X
0 = I
{ < x007D;–x ( is uniformly distributed on [0, 1]), whichtakes its values in H = L
2[0,1], and in a sense generates the so-called2-statistic. It is shown in the present paper thatX
0 does not satisfy the condition of Nagaev andChebotarev,(11) and also, at least partly, thecondition of Bentkus.(2, 3)
One more versionof the Cramér condition in the case of Hilbert space is suggestedin the paper not for individual summands, but for the whole sum. Ageneralization of the estimate of the characteristic function of squarednorm of the sum of independent truncations is obtained in terms ofquantities, which define this modification. It is shown thatX
0 satisfies this version of the Cramércondition. 相似文献
997.
J. Sunklodas 《Acta Appl Math》1999,58(1-3):327-341
We derive a lower bound of the uniform distance in the central limit theorem for real -mixing random variables under the finiteness of the eighth moments of summands. The main result of the present paper generalizes the corresponding author"s result obtained in 1997 for m-dependent random variables to the case of -mixing random variables. 相似文献
998.
A. Astrauskas 《Lithuanian Mathematical Journal》1999,39(2):117-133
Let
, be the mean-field Hamiltonian with
and random i.i.d. potential ξV. We prove limit theorems for the extreme eigenvalues of
as |V|→∞. The limiting distributions are the same as for the corresponding extremes of ξV only if either (i) ξV is undbounded and
, or (ii) ξV is bounded with “sharp” peaks and
. Localization properties for the corresponding eigenfunctions are also studied.
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys,
Vol. 39, No. 2, pp. 147–168, April–June, 1999. 相似文献
999.
环R称为半零可换的,如果由a,b∈R,ab=0可推出存在正整数n使得b~na=0.本文证明了R为半零可换环当且仅当Sn(R)为半零可换环,其中n≥2为任意整数,从而肯定地回答了Roy和Subedi在[Asian-Eur.J.Math.,2021,14(2):2150018,11 pp.]中提出的一个问题.本文还证明了R是弱零可换环当且仅当R是弱半交换环,而R是J-零可换环当且仅当R是J-半交换环. 相似文献
1000.
本文研究具有高阶导子的莱布尼兹代数.我们称之为LeibHDer对.首先给出LeibHDer对的表示并构造半直积.最后,定义LeibHDer对的上同调并研究其中心扩张和形变理论. 相似文献