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A simple approach to the generation of uniformly distributed random variables with prescribed correlations

 Titel: A simple approach to the generation of uniformly distributed random variables with prescribed correlations Auteur: Falk, Michael Verschenen in: Communications in statistics Paginering: Jaargang 28 (1999) nr. 3 pagina's 785-791 Jaar: 1999 Inhoud: In a simulation study we encountered the problem of generating uniformly on (0,1) distributed random variables with a prescribed correlation matrix. This article reports our solution to this problem.We show that the following simple device leads to uniformly on (0,1)distributed random variables, which have a correlation matrix that isfor practical purposes sufficiently close to the prescribed one: Let(X1.., Xm) be a normal vector with theprescribed correlation matrix S = (pij:). Such a vector caneasily be generated. Suppose for simplicity that each Xi is standard normal and denote by Φ the standard normal distribution function. It turns out that the vector(V1:…,Vm:):= (φ(X1),…,φ(Xm)) with uniformly on (0,1)distributed components Vi; then has a correlation matrix S', whose entries are for practical purposes sufficiently close to that of the target matrix S. This is a consequence of the grade correlation (or Spearman's rho) of normal vectors. Suppose, in addition, that the matrix [image omitted]  is positive semidefinite. Then the vectors [image omitted]  , with [image omitted]  ; being standard normal and [image omitted]  ,being normal with correlation matrix [image omitted]  , has exact correlation matrix S. The matrix [image omitted]  is, however, not in general positive semidefinite. Uitgever: Taylor & Francis Bronbestand: Elektronische Wetenschappelijke Tijdschriften

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