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Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing
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abstract
The following anticoncentration property is proved. The probability that the $k$-order statistic of an arbitrarily correlated jointly Gaussian random vector $X$ with unit variance components lies within an interval of length $\varepsilon$ is bounded above by $2{\varepsilon}k ({ 1+\mathrm{E}[\|X\|_\infty ]}) $. This bound has implications for generalized error rate control in statistical high-dimensional multiple hypothesis testing problems, which are discussed subsequently.
Forward citations
Cited by 2 Pith papers
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Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics
Provides Gaussian multiplier bootstrap approximation error bounds for the kth largest coordinate of high-dimensional statistics, valid when dimension exceeds sample size.
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Sharp Anti-Concentration Inequalities for Extremum Statistics via Copulas
For maxima of identically distributed random variables, the paper gives sharp anti-concentration bounds under arbitrary dependence, and sharper bounds under a new convexity condition on the copula's diagonal.
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