Abstract:
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.
Keywords:
limit theorems, stochastic integral, multiple stochastic integral, elementary stochastic measure, Gaussian processes, stationary sequences of random variables, mixing, U- and V-statistics.
Citation:
I. S. Borisov, A. A. Bystrov, “Limit theorems for the canonical von Mises statistics with dependent data”, Sibirsk. Mat. Zh., 47:6 (2006), 1205–1217; Siberian Math. J., 47:6 (2006), 980–989
\Bibitem{BorBys06}
\by I.~S.~Borisov, A.~A.~Bystrov
\paper Limit theorems for the canonical von Mises statistics with dependent data
\jour Sibirsk. Mat. Zh.
\yr 2006
\vol 47
\issue 6
\pages 1205--1217
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\zmath{https://zbmath.org/?q=an:1150.60324}
\transl
\jour Siberian Math. J.
\yr 2006
\vol 47
\issue 6
\pages 980--989
\crossref{https://doi.org/10.1007/s11202-006-0109-3}
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Linking options:
https://www.mathnet.ru/eng/smj929
https://www.mathnet.ru/eng/smj/v47/i6/p1205
This publication is cited in the following 9 articles:
I. S. Borisov, S. E. Khrushchev, “Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes”, Siberian Adv. Math., 26:1 (2016), 1–16
Denker M., Gordin M., “Limit Theorems For Von Mises Statistics of a Measure Preserving Transformation”, Probab. Theory Relat. Field, 160:1-2 (2014), 1–45
Leucht A., Neumann M.H., “Degenerate - and -Statistics Under Ergodicity: Asymptotics, Bootstrap and Applications in Statistics”, Ann. Inst. Stat. Math., 65:2 (2013), 349–386
I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical U- and V-statistics based on dependent observations”, Siberian Adv. Math., 25:1 (2015), 21–32
Ferger D., Scholz M., “Limit distributions of V- and U-statistics in terms of multiple stochastic Wiener-type integrals”, J Multivariate Anal, 102:2 (2011), 306–314
I. S. Borisov, V. A. Zhechev, “The functional limit theorem for the canonical U-processes defined on dependent trials”, Siberian Math. J., 52:4 (2011), 593–601
N. V. Volod'ko, “Limit theorems for canonical von Mises statistics and U-statistics for m-dependent observations”, Theory Probab. Appl., 55:2 (2011), 271–290
I. S. Borisov, N. V. Volodko, “Orthogonal series and limit theorems for canonical U- and V-statistics of stationary connected observations”, Siberian Adv. Math., 18:4 (2008), 242–257
I. S. Borisov, N. V. Volodko, “Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations”, Siberian Adv. Math., 19:1 (2009), 1–12
Citation in format AMSBIB
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