A Consistent Test for Bivariate Dependence

By Andrey Feuerverger. 1993

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Citations in the corpus

Kernel‐based tests for joint independence (2016, methodology): “Consistent pairwise non-parametric independence tests date back to Feuerverger (1993) and Romano (1986) and have more recently received considerable attention by using kernel-based methods (Gretton et al.”
A Kernel Method for the Two-Sample-Problem (2006, background): “ RKHSs with Gaussian kernels, the empirical ∆2 may also be interpreted in terms of a smoothed diﬀerence between the joint empirical characteristic function (ECF) and the product of the marginal ECFs (Feuerverger, 1993; Kankainen, 1995). This interpretation does not hold in all cases, however, e.g. f”
Discussion of: Brownian distance covariance (2009, background): “A further difference of Kankainen (1995) with respect to Feuerverger (1993) is that Kankainen generalizes to the problem of testing mutual independence, although the variables themselves remain univariate.”
An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, unknown): “More on the comparison between the distance covariance and the statistics proposed by Feuerverger (1993) can be found in Gretton et al. (2009).”
Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence (2005, background): “Despite the anticipation that the Cramér–von Mises statistic ∫ H2n dHn should be powerful, most subsequent research focused on the case d = 2, where alternative tests, typically based on moment characterizations of independence, were proposed, for example, by Feuerverger [9], Shih and Louis [21], G”
A Kernel Two-Sample Test (2012, background): “In certain circumstances, including in the case of RKHSs with Gaussian kernels, the empirical∆2 may also be interpreted in terms of a smoothed difference between the joint empirical characteristic function (ECF) and the product of the marginal ECFs (Feuerverger, 1993; Kankainen, 1995).”
A consistent modification of a test for independence based on the empirical characteristic function (1998, methodology): “Note that transformations of this kind have been already used in [ 7 ] and [9].”
Partial Distance Correlation with Methods for Dissimilarities (2013, unknown): “Note that Feuerverger (1993) [5] proposed a bivariate test based on this idea and applied the same weight function w , where it may have ﬁrst appeared.”
Supervised feature selection via dependence estimation (2007, background): “See [6] for a different interpretation of a related criterion used in independence testing.”
A consistent test of independence based on a sign covariance related to Kendall's tau (2010, methodology): “The expression (11) was originally introduced by Feuerverger [8], but only for real X and Y (p = q = 1).”
A Kernel Statistical Test of Independence (2007, methodology): “One approach, taken by [6], is to use a Monte Carlo resampling technique: the ordering of the Y sample is permuted repeatedly while that of X is kept fixed, and the1 − α quantile is obtained from the resulting distribution of HSICb values.”
A Hilbert Space Embedding for Distributions (2007, background): “In certain circumstances, including in the case of RKHSs with Gaussian kernels, the empirical ∆ 2 may also be interpreted in terms of a smoothed difference between the joint empirical characteristic function (ECF) and the product of the marginal ECFs [46, 47].”
Applications of distance correlation to time series (2016, methodology): “The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and Mureika (1977), Csörgő (1981a,1981b,1981c) Feuerverger (1993)). ”
A multivariate nonparametric test of independence Nail (2006, background): “More recently, Feuerverger [4] proposed a consistent bivariate rank test of independence.”