B1328
Title: Maximum likelihood estimation of a covariance matrix with thresholding: Application to Huntington disease
Authors: Tanya Garcia - UNC Chapel Hill (United States) [presenting]
Rakheon Kim - Texas AM University (United States)
Mohsen Pourahmadi - Texas A and M University (United States)
Abstract: The covariance matrix for a multivariate normal distribution is estimated when some entries of the matrix are zero. Compared to some existing methods such as thresholding, a positive-definite and asymptotically efficient estimator does not lose validity as a covariance matrix and provides higher confidence in estimation. However, such an estimator can be obtained only when the location of the zero entries is correctly identified. Moreover, even when the location of the zero entries is known, current approaches may fail to guarantee either positive-definiteness or asymptotic efficiency. We show that a positive-definite and asymptotically efficient estimator can always be computed by iterative conditional fitting when the location of the zero entries is known. Also, when the location of the zero entries is unknown, we propose a positive-definite thresholding estimator by combining iterative conditional fitting with thresholding and show that it is asymptotically efficient with probability tending to one. In simulation studies, the proposed estimator detected more non-zero covariances correctly, having a lower distance to the true covariance matrix than other thresholding estimators. Application to Huntington disease data detected non-zero correlations among brain regional volumes, informing which brain regions would be affected by a treatment for the disease
