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.
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Original Russian Text Copyright © 2006 Borisov I. S. and Bystrov A. A.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 6, pp. 1205–1217, November–December, 2006.
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Borisov, I.S., Bystrov, A.A. Limit theorems for the canonical von Mises statistics with dependent data. Sib Math J 47, 980–989 (2006). https://doi.org/10.1007/s11202-006-0109-3
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DOI: https://doi.org/10.1007/s11202-006-0109-3