Generating random correlation matrices by the simple rejection method: why it does not work. (English) Zbl 1298.65077
Summary: We derive exact and asymptotic formulas for the probability that a symmetric \(n{\times}n\) matrix with unit diagonal and upper diagonal elements i.i.d. uniform on \((-1,1)\) is positive definite (and thus a “random correlation matrix”): this is almost never the case for \(n\geq 6\).
MSC:
| 65F30 | Other matrix algorithms (MSC2010) |
| 15B52 | Random matrices (algebraic aspects) |
| 65C60 | Computational problems in statistics (MSC2010) |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
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