Orthogonal series and limit theorems for canonical U-and V-statistics of stationary connected observations

The limit behavior is studied for the distributions of normalized U -and V -statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying φ -or α -mixing. The corresponding limit distributions are repr...

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Bibliographic Details
Published in:Siberian advances in mathematics 2008, Vol.18 (4), p.242-257
Main Authors: Borisov, I. S., Volodko, N. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:The limit behavior is studied for the distributions of normalized U -and V -statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying φ -or α -mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.
ISSN:1055-1344
1934-8126
DOI:10.3103/S1055134408040020