Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm
نویسنده
چکیده
cosine of angle ij θ between the vectors . i j x and x An arbitrary real symmetric matrix, Q (defined above), is not a genuine product moment correlation matrix obtainable from some real X although it may appear to be so. Such negative semidefinite (nsd) or pseudocorrelation matrices may enter into empirical investigation due to several reasons. First, the coefficients of correlation may not be computed by the Karl Pearson’s (product moment) formula. They might have been obtained by Spearman’s formula (of rank correlation) or they could be the polychoric coefficients of correlation. Secondly, some of them might have been computed from variables different in sample size (observations). Suppose
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