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Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing

by   Damian Kozbur, et al.
Universität Zürich

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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