Orthogonal series and limit theorems for canonical U- and V-statistics of stationary connected observations
By I.S.Borisov, N.Volodko. 2009
12 citations recorded by the source corpus.
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 φor α-mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix. keywords: stationary sequence of random variables, mixing, multiple orthogonal series, canonical U and V -statistics.
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Citations in the corpus
- A Wild Bootstrap for Degenerate Kernel Tests (2014, background): “Unfortunately, the limiting distribution of such V -statistics is quite complicated - it is an infinite sum of dependent χ(2)-distributed random variables, with a dependence determined by the temporal dependence structure within the process {Zt} and by the eigenfunctions of a certain integral operat”
- Degenerate $$U$$- and $$V$$-statistics under ergodicity: asymptotics, bootstrap and applications in statistics (2013, methodology): “As pointed out by Borisov and Volodko (2008), approximation (1) is valid for almost all (x ′, y′)′ ∈ supp(P X0 ⊗ P X0).”