Selected-target noncoverage after black-box selection is bounded by nominal fixed-target noncoverage plus average total variation distance between marginal and conditional laws of the inferential data.
(2002).Foundations of Modern Probability
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A Leakage Bound for Confidence Sets after Black-Box Selection
Selected-target noncoverage after black-box selection is bounded by nominal fixed-target noncoverage plus average total variation distance between marginal and conditional laws of the inferential data.