Nonlinear canonical analysis and independence tests

By J. Dauxois, G. Nkiet. 1998

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Citations in the corpus

A low variance consistent test of relative dependency (2014, background): “The statistics for such tests are diverse, and include kernel measures of covariance [5, 19] and correlation [2, 3], distance covariances (which are instances of kernel tests) [18, 14], rankings [7], and space partitioning approaches [6, 12, 9].”
A Kernel Test for Three-Variable Interactions (2013, background): “Much of the work in this area focuses on measuring or testing pairwise interaction: for instance, the Hilbert-Schmidt Independence Criterion (HSIC) or Distance Covariance [1, 2, 3], kernel canonical correlation [4, 5, 6], and mutual information [7].”
Kernel methods in machine learning (2007, neutral): “In Bach and Jordan [8], Das and Sen [41], Dauxois and Nkiet [42] and Gretton et al. [58, 59] a constrained empirical estimate of the above criterion is used.”
Kernel Methods for Measuring Independence (2005, methodology): “(1993) for the operator norm, and by Fukumizu et al. (2005) for the functions in F and G that define it (in accordance with Definition 7 below).”
Consistent Nonparametric Tests of Independence (2010, methodology): “Dauxois and Nkiet (1998) propose the canonical correlation between variables in a spline-based RKHS as a statistic for an independence test: this dependence measure follows the suggestion of Rényi (1959), but with a more restrictive pair of function classes used to compute the correlation (rather…”
Discussion of: Brownian distance covariance (2009, result): “…were based on the canonical correlation, rather than the covariance: in this respect, they more strongly resemble the statistic R 2 n of SR. Dauxois and Nkiet (1998) propose the canonical correlation between variables in a spline-based RKHS as a dependence measure, using projection on a…”
Strongly consistent nonparametric tests of conditional independence (2012, background): “As further literature we mention Bakirov et al. (2006), Beran et al. (2007), Dauxois and Nkiet (1998), Fukumizu et al. (2007), Gieser and Randles (1997), Gretton et al. (2005), Kankainen (1995), Genest et al. (2007), Dette and Neumeyer (2000) with references.”
Testing conditional independence using maximal nonlinear conditional correlation (2010, methodology): “The difference is that the asymptotic result here is derived as the sample size n, pn and qn all tend to ∞, while in [3], the result is derived as n tends to ∞, but pn and qn are held fixed.”
A Kernel Statistical Test of Independence (2007, methodology): “The approach in [4] differs with both the present work and [2], however, in that the function spaces F andG are represented by finite sets of basis functions (specifically B-spline kernels) when computing the empirical test statistic.”
Large-scale kernel methods for independence testing (2016, background): “The functions of the spectra that were considered in [11] are very general, but the simplest one (sum of the squared singular values) can be recast as the NOrmalised Cross-Covariance Operator (NOCCO) of [13], which considers the Hilbert-Schmidt norm of the cross-correlation operator on RKHSs and as…”