Statistical Corrections of Invalid Correlation Matrices


  • Journal: Scandinavian Journal of Statistics, vol. 40, p. 807–824–18, 2013
  • Internasjonale standardnumre:
    • Trykt: 0303-6898
    • Elektronisk: 1467-9469
  • Lenke:

Suppose estimates are available for correlations between pairs of variables but that the matrix of correlation estimates is not positive definite. In various applications, having a valid correlation matrix is important in connection with follow-up analyses that might, for example, involve sampling from a valid distribution. We present new methods for adjusting the initial estimates to form a proper, that is, nonnegative definite, correlation matrix. These are based on constructing certain pseudo-likelihood functions, formed by multiplying together exact or approximate likelihood contributions associated with the individual correlations. Such pseudo-likelihoods may then be maximized over the range of proper correlation matrices. They may also be utilized to form pseudo-posterior distributions for the unknown correlation matrix, by factoring in relevant prior information for the separate correlations. We illustrate our methods on two examples from a financial time series and genomic pathway analysis.