Abstract:
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The notion of simplicial depth was introduced by Liu (1988, 1990) and at about the same time the notion of interdirections was introduced by Randles (1989). These completely independent and seemingly unrelated initiatives, having different purposes, have spawned significant activity in their quite different respective domains. Here we exhibit a surprising connection between the two notions and discuss fruitful applications of this finding. In particular, procedures involving interdirections can be expressed in terms of simplicial depth, with greater conceptual appeal and lesser computational burden. Sign test statistics are discussed in detail, and other applications are proposed.
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