Limit theorems for the canonical von Mises statistics with dependent data

被引：0
作者：
I. S. Borisov
A. A. Bystrov
机构：
[1] Sobolev Institute of Mathematics,
来源：
Siberian Mathematical Journal | 2006年 / 47卷
关键词：
limit theorems; stochastic integral; multiple stochastic integral; elementary stochastic measure; Gaussian processes; stationary sequences of random variables; mixing; -and ; -statistics;
D O I：
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学科分类号：
摘要：
We study the limit behavior of the canonical (i.e., degenerate) von Mises statistics based on samples from a sequence of weakly dependent stationary observations satisfying the ψ-mixing condition. The corresponding limit distributions are defined by the multiple stochastic integrals of nonrandom functions with respect to the nonorthogonal Hilbert noises generated by Gaussian processes with nonorthogonal increments.
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页码：980 / 989
页数：9
相关论文
共 21 条
  • [1] Borisov I. S.(2006)Constructing a stochastic integral of a nonrandom function without orthogonality of the noise Theory Probab. Appl. 50 53-74
  • [2] Bystrov A. A.(1947)On the asymptotic distribution of differentiable statistical functions Ann. Math. Statist. 18 309-348
  • [3] Von Mises R.(1948)A class of statistics with asymptotically normal distribution Ann. Math. Statist. 19 293-325
  • [4] Hoeffding W.(2000)The central limit theorem for generalized canonical von Mises statistics Siberian Adv. Math. 10 1-14
  • [5] Borisov I. S.(1962)Von Mises’ theorem on the limit behavior of functionals of the empirical distribution functions and its statistical applications Theory Probab. Appl. 7 26-60
  • [6] Sakhanenko L. A.(1951)Multiple Wiener integral J. Math. Soc. Japan 3 157-169
  • [7] Filippova A. A.(1983)Symmetric statistics, Poisson point processes and multiple Wiener integrals Ann. Statist. 11 739-745
  • [8] Itô K.(1979)Orthogonal expansions and Austral. J. Statist. 21 221-237
  • [9] Dynkin E. B.(1980)-statistics Ann. Statist. 8 165-170
  • [10] Mandelbaum A.(1989)Asymptotic distribution of symmetric statistics Ann. Statist. 17 1767-1783
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