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Moment inequalities for the partial sums of random variables 总被引:2,自引:0,他引:2
杨善朝 《中国科学A辑(英文版)》2001,44(1):1-6
This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B
type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random
variables are obtained. 相似文献
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Iosif Pinelis 《Probability Theory and Related Fields》2007,139(3-4):605-635
Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter
. Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in .
A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales
with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications
to generalized self-normalized sums and t-statistics are given.
相似文献
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V.V Yurinskiĭ 《Journal of multivariate analysis》1976,6(4):473-499
This paper presents some generalizations of S. N. Bernstein's exponential bounds on probabilities of large deviations to the vector case. Inequalities for probabilities of large deviations of sums of independent random vectors are derived under a Cramér's type restriction on the rate of growth of absolute moments of the summands. Estimates are obtained for random vectors with values in Banach space, Sharper bounds hold in the case of finite-dimensional Euclidean or separable Hilbert spaces. 相似文献
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Probability and moment inequalities for sums of weakly dependent random variables,with applications 总被引:1,自引:0,他引:1
Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313–342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics. 相似文献
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Periodica Mathematica Hungarica - Maximal inequalities for the signed vector summands are established. Probabilistic estimations for the sets of appropriate signs are given. By use of the... 相似文献
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N. Yu. Kryzhanovskaya 《Mathematical Notes》2008,83(5-6):770-782
We study a real random field defined on an integer lattice. Its dependence is described by certain covariance inequalities. We obtain an upper bound of absolute moments of appropriate order for particular sums (generated by a given field) taken over finite sets of arbitrary configuration. 相似文献
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Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 3, pp. 426–434, July–September, 1992. 相似文献
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Lixin Zhang 《中国科学A辑(英文版)》1998,41(7):736-745
Some inequalities for moments of partial sums of aB -valued strong mixing field are established and their applications to the weak and strong laws of large numbers and the complete
convergences are discussed.
Project supported by the National Natural Science Foundation of China (Grant No. 19701011) and China Postdoctoral Science
Foundation. 相似文献
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NA序列部分和的矩完全收敛性 总被引:4,自引:0,他引:4
讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果. 相似文献
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Yongge Tian 《Linear algebra and its applications》2010,433(1):263-296
The inertia of a Hermitian matrix is defined to be a triplet composed of the numbers of the positive, negative and zero eigenvalues of the matrix counted with multiplicities, respectively. In this paper, we show some basic formulas for inertias of 2×2 block Hermitian matrices. From these formulas, we derive various equalities and inequalities for inertias of sums, parallel sums, products of Hermitian matrices, submatrices in block Hermitian matrices, differences of outer inverses of Hermitian matrices. As applications, we derive the extremal inertias of the linear matrix expression A-BXB∗ with respect to a variable Hermitian matrix X. In addition, we give some results on the extremal inertias of Hermitian solutions to the matrix equation AX=B, as well as the extremal inertias of a partial block Hermitian matrix. 相似文献
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In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides.
The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob’s type
maximal inequality for demimartingales, strong laws of large numbers and growth rate for demimartingales and associated random
variables. At last, we give an equivalent condition of uniform integrability for demisubmartingales. 相似文献
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S. B. Shlosman 《Journal of Mathematical Sciences》1981,15(2):79-101
Correlation inequalities and their applications to the question of the presence or absence of phase transitions is classical lattice systems are considered. A major part of the known inequalities is obtained as a corollary of a single general theorem.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 16, pp. 5–37, 1979. 相似文献
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Talagrand’s inequalities provide a link between two fundamentals concepts of probability: transportation and entropy. The study of the counterpart of these inequalities in the context of free probability has been initiated by Biane and Voiculescu and later extended by Hiai, Petz and Ueda for convex potentials. In this work, we prove a free analogue of a result of Bobkov and Götze in the classical setting, thus providing free transport-entropy inequalities for a very natural class of measures appearing in random matrix theory. These inequalities are weaker than the ones of Hiai, Petz and Ueda but still hold beyond the convex case. We then use this result to get a concentration estimate for $\beta $ -ensembles under mild assumptions on the potential. 相似文献