# New perspectives on knockoffs construction

Let Λ be the collection of all probability distributions for (X,X), where X is a fixed random vector and X ranges over all possible knockoff copies of X (in the sense of <cit.>). Three topics are developed in this note: (i) A new characterization of Λ is proved; (ii) A certain subclass of Λ, defined in terms of copulas, is introduced; (iii) The (meaningful) special case where the components of X are conditionally independent is treated in depth. In real problems, after observing X=x, each of points (i)-(ii)-(iii) may be useful to generate a value x for X conditionally on X=x.

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