BEAUTY Powered BEAST
- URL: http://arxiv.org/abs/2103.00674v5
- Date: Mon, 16 Oct 2023 15:39:02 GMT
- Title: BEAUTY Powered BEAST
- Authors: Kai Zhang, Zhigen Zhao, Wen Zhou
- Abstract summary: We study distribution-free goodness-of-fit tests with the proposed Binary Expansion Approximation of UniformiTY (BEAUTY) approach.
We demonstrate that the Neyman-Pearson test of uniformity can be approximated by an oracle weighted sum of symmetry statistics.
- Score: 6.29096297476023
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study distribution-free goodness-of-fit tests with the proposed Binary
Expansion Approximation of UniformiTY (BEAUTY) approach. This method
generalizes the renowned Euler's formula, and approximates the characteristic
function of any copula through a linear combination of expectations of binary
interactions from marginal binary expansions. This novel theory enables a
unification of many important tests of independence via approximations from
specific quadratic forms of symmetry statistics, where the deterministic weight
matrix characterizes the power properties of each test. To achieve a robust
power, we examine test statistics with data-adaptive weights, referred to as
the Binary Expansion Adaptive Symmetry Test (BEAST). Using properties of the
binary expansion filtration, we demonstrate that the Neyman-Pearson test of
uniformity can be approximated by an oracle weighted sum of symmetry
statistics. The BEAST with this oracle provides a useful benchmark of feasible
power. To approach this oracle power, we devise the BEAST through a regularized
resampling approximation of the oracle test. The BEAST improves the empirical
power of many existing tests against a wide spectrum of common alternatives and
delivers a clear interpretation of dependency forms when significant.
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