Vitenskapelig artikkel   2013

Løland, Anders; Huseby, Ragnar Bang; Hjort, Nils Lid; Frigessi, Arnoldo

Publication details

Journal:

Scandinavian Journal of Statistics, vol. 40, p. 807–824–18, 2013

Issue:

4

International Standard Numbers:

Printed: 0303-6898
Electronic: 1467-9469

Links:

DOI: doi.org/10.1111/sjos.12035

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.