Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing
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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 ε is bounded above by 2εk ( 1+E[X_∞ ]). This bound has implications for generalized error rate control in statistical high-dimensional multiple hypothesis testing problems, which are discussed subsequently.
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