Abstract
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 Candes et al. (2018)). Three topics are developed in this paper: (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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