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.
Tijdschrift beschrijving