Multiscale Fisher's Independence Test for Multivariate Dependence

Gorsky, Shai; Ma, Li

doi:10.48550/arxiv.1806.06777

Cited by 2 publications

(3 citation statements)

References 16 publications

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“…Although the test based on Spearman's ρ has a higher power against the linear form of dependency particularly present in bivariate normal distributions, we see from (Ma and Mao, 2019). Multivariate extensions of these methods include Gorsky and Ma (2018); Lee et al (2019).…”

Section: Spearman's ρmentioning

confidence: 81%

BEAUTY Powered BEAST

Zhang,

Zhao,

Zhou

2021

Preprint

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We study inference about the uniform distribution with the novel binary expansion approximation of uniformity (BEAUTY) approach. Through an extension of the celebrated Euler's formula, we approximate the characteristic function of any copula distribution with a linear combination of means of binary interactions from marginal binary expansions. This novel characterization enables a unification of many important existing tests through an approximation from some quadratic form of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a uniformly high power, we study test statistics with data-adaptive weights through an oracle approach, referred to as the binary expansion adaptive symmetry test (BEAST). By utilizing the properties of the binary expansion filtration, we show that the Neyman-Pearson test of uniformity can be approximated by an oracle weighted sum of symmetry statistics. The BEAST with this oracle leads all existing tests we considered in empirical power against all complex forms of alternatives. By approximating this oracle with data-adaptive weights, we develop the BEAST that improves the empirical power of many existing tests against a wide spectrum of common alternatives while providing clear interpretation of the form of non-uniformity upon rejection.

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Section: Spearman's ρmentioning

confidence: 81%

BEAUTY Powered BEAST

Zhang,

Zhao,

Zhou

2021

Preprint

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“…An important step towards this goal is to be able to test if (X, Y ) is uniform, or alternatively at what resolutions we have sufficient power to make a rejection. We adopt the notation of Gorsky and Ma (2018). For a joint sample space Ω = Ω x × Ω y it is possible to create a coarse-to-fine discretization of Ω.…”

Section: Ds Test Of Independencementioning

confidence: 99%

“…One general approach in nonparametric tests of independence is the multi-resolution approach. See some recent work by Ma and Mao (2019); Zhang (2019); Lee et al (2019); Gorsky and Ma (2018); Zhang et al (2021). Some advantages of this approach include uniform consistency, minimax optimal power, clear interpretability and efficient computation.…”

Section: Introductionmentioning

confidence: 99%

Comments on: A Gibbs sampler for a class of random convex polytopes

Hoffman,

Hannig,

Zhang

2021

Preprint

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Multiscale Fisher's Independence Test for Multivariate Dependence

Cited by 2 publications

References 16 publications

BEAUTY Powered BEAST

BEAUTY Powered BEAST

Comments on: A Gibbs sampler for a class of random convex polytopes

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