The strong law of large numbers for u-statistics.

By W. Hoeffding. 1961

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Citations in the corpus

Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “The pioneering work of Hooker and Vidyashankar (2014) and Ghosh and Basu (2016) established Bernstein–von Mises results for generalised posteriors defined by α- and β-divergences.”
A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data (2013, background): “By the Strong Law of Large Numbers for U-statistics, we have that with probability 1, ∃N1 ∈ N such that∣∣∣∣∣ ( # 1 2 )−1 ∑ 1 |Zi − Zj |α − μαX ∣∣∣∣∣ < whenever # 1 > N1.”
ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data (2013, background): “By the strong law of large numbers for U -statistics (Hoeffding, 1961) Ê(Xn,Y m;α) a.”
Asymptotic theory for stationary processes (2011, methodology): “Hoeffding (1961), O’Neil and Redner (1993), Major (1994) and Rifi and Utzet (2000) considered properties of Un for iid observations.”
Independent Component Analysis via Distance Covariance (2013, methodology): “For each k , 3 and the continuous mapping theorem, and by Assumption 2.1, the triangle inequality, H¨older’s inequality, the strong law of large numbers for U -statistics (see Hoeﬀding 1961), and Slutsky’s theorem, as n →∞ , thus establishing the assertion.”
A constructive approach to the estimation of dimension reduction directions (2007, background): “Hoeffding, 1961 ), � (1) = R ρ(f(x))ρ(f Y (y)) ▽ gb0 (B ⊤ x, y) ▽ ⊤ gb0 (B ⊤ 0 x, y)}f(x) f Y (y)dxdy + o(1) al-”
Limit theorems for functionals of mixing processes with applications to U-statistics and dimension estimation (2001, background): “Already Hoeffding established asymptotic normality of U -statistics in the case of i.i.d. observations.”