Some properties of incomplete U-statistics

By Guninar Blom. 1976

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, neutral): “…k(x,x′) = ψ(x − x′) for some positive definite function ψ on Rd, we have MMD(H ,P,Q) = ∫ Rd |ϕP(ω)− ϕQ(ω)|2F−1[ψ(ω)] dω (3.34) where F−1[·] denotes the inverse Fourier transform and ϕP, ϕQ are 7The B-test can be understood as a specific case of the tests using incomplete U -statistic (Blom 1976).”
Generalized Fiducial Inference: A Review and New Results (2016, background): “Blom (1976) showed that incomplete U -statistic based on random selection of K subsamples behaves very similar to the complete U -statistic when n and K are large.”
On U-statistics and v. mise’ statistics for weakly dependent processes (1983, background): “2 do not depend very much on these index sets, so it is possible to consider incomplete U-statistics in the sense of Blom [ 3 ] or reduced U-statistics in the sense of Brown and Kildea [7].”
RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES (2012, methodology): “This method and compromises between it and the (;:J bootstrap are studied in Blom (1976) for instance. The (~) bootstrap differs from the mjn by op(1) if m = o(n112 ). Its advantage is that it never presents us with the ties which make resampling not look like sampling. As a consequence, as we note ”
Ensemble Trees and CLTs: Statistical Inference for Supervised Learning (2014, unknown): “For incomplete U-statistics of ﬁxed rank, Blom [1976] showed that the variance of the incomplete U-statistic U m consisting of m subsamples selected uniformly at random with replacement is given by where U is the complete U-statistic analogue.”
Model selection in high dimensions: a quadratic‐risk‐based approach (2006, background): “, 2004), or randomly selected subsets of size m (Blom, 1976).”