On the Bootstrap of $U$ and $V$ Statistics

By Miguel A. Arcones, Evarist Gin'e. 1992

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In Statistics and Probability

Citations in the corpus

A Sober Look at the Unsupervised Learning of Disentangled Representations and their Evaluation (2020, background): “Samples from ∏d j=1 q(zj) can be obtained shuffling samples from q(z) (Arcones and Gine, 1992).”
Learning Representations by Maximizing Mutual Information in Variational Autoencoders (2019, neutral): “This trick is first used in [22], and proved to be sufficiently accurate as long as the batch size is large enough, i.”
Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations (2018, background): “Samples from ∏d j=1 q(zj) can be obtained shuffling samples from q(z) (Arcones & Gine, 1992).”
Disentangling by Factorising (2018, methodology): “This is a standard trick used in the independence testing literature [1, 6].”
A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “In this work, we adopt the bootstrap method suggested in Huskova & Janssen (1993); Arcones & Gine (1992): We repeatedly draw multinomial random weights ( w 1 , . . . w n ) ∼ Mult( n ; 1 n , . . . , 1 n ) , and calculate boot-strap sample and then calculate the empirical quantile ˆ γ 1 − α of n ˆ S…”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “The bootstrap strategy (Arcones & Giné, 1992) is utilized in our experiments since it can be easily integrated into our FastMMD method.”
Hypothesis testing using pairwise distances and associated kernels (2012, methodology): “We investigate two approaches, both of which yield consistent tests: a bootstrap approach (Arcones & Giné, 1992), and a spectral approach (Gretton et al., 2009a; Zhang et al., 2011).”
Randomized numerical linear algebra: Foundations and algorithms (2020, methodology): “See Arcones and Gine (1992) for reliable bootstrap procedures for U -statistics.”
An anova test for functional data (2004, methodology): “This problem has been already considered by Fan and Lin (1998) in the case when the sampling information is in a “discrete” format Xij(t), t=1; : : : ; T . They propose a useful HANOVA (high dimensional anova) test, relying on wavelet thresholding techniques. A di9erent approach is given by Muñoz-Ma”
Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems (2012, methodology): “The first main contribution of our work at this stage consists in proposing a new choice for the critical values, based on wild or permutation bootstrap approaches, thus following the original ideas of Mammen (1992) and Bickel (1968), but applied to U -statistics as in Arcones and Giné (1992). This ”
Consistency of general bootstrap methods for degenerate U-type and V-type statistics (2009, unknown): “Available results of general type include those of Bickel and Freedman [1] for Efron’s bootstrap applied to linear and related statistics, Arcones and Giné [2] for Efron’s bootstrap in connection with U- and V -statistics, and Stute, GonzálezManteiga and PresedoQuindimil [3]who showed that the boots”
A Hilbert Space Embedding for Distributions (2007, methodology): “In [16], this was achieved via two strategies: by using the bootstrap [34], and by fitting Pearson curves using the first four moments [35, Section 18.”
ABX-Discriminability Measures and Applications. (Mesures de discriminabilité ABX et applications) (2016, background): “4 and subsequent remarks of [239], we obtain that ˆ”
Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications (2016, methodology): “For univariate U-statistics, the empirical bootstrap was studied in [7, 2] and the randomly reweighted bootstrap of the form (15) was proposed in [42, 40], where a different class of random weights wi was considered satisfying wi = ξi/(n −1∑n i=1 ξi) such that ξi are iid non-negative random variable”