In structural equation modeling (SEM), a covariance parameter is derived by minimizing the discrepancy between a sample covariance matrix and a covariance matrix having a specified structure. When a sample covariance matrix is a near singular matrix, Yuan and Chan (2008) proposed the use of an adjusted sample covariance matrix instead of the sample covariance matrix in the discrepancy function ...

For statistical inferences that involve covariance matrices, it is desirable to obtain an accurate covariance matrix estimate with a well-structured eigen-system. We propose to estimate the covariance matrix through its matrix logarithm based on an approximate log-likelihood function. We develop a generalization of the Leonard and Hsu (1992) log-likelihood approximation that no longer requires ...

Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When theoretical model for the matrix exists, parameters can fit with many fewer simulations. We write likelihood-based method performing such fit. demonstrate how tested by examining appropriate $\chi^2$ distr...

Cleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference dependence between objects. We propose here probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC), that particularly effective high-dimensional case, i.e., when there are more objects than features. When applied to DNA microarray,...