Mohsen Pourahmadi (Texas A&M University, Department of Statistics)
Title: Modeling Structured Correlation Matrices
There has been a flurry of activity in the last two decades in model- ing/reparametrizing correlation matrices going beyond the familiar Fisher z-transform of a single correlation coefficient. We present an overview of the developments focusing on reparametrizing Cholesky factors of correlation matrices using hyperspherical coordinates where the ensuing angles are meaningful geometrically. In spite of the lack of broadly accepted statistical interpretation, we demonstrate that these angles are quite flexible and effective for parsimonious modeling of large nearly block-structured correlation matrices commonly encountered in finance, environmental and biological sciences. Asymptotic nor- mality of the maximum likelihood estimates of these angles as new parameters is estab- lished. Real examples will be used to demonstrate the flexibility and applicability of the methodology. The role of an order among the variables and connection with the recent surge of interest in sparse estimation of directed acyclic graphs (DAG) will be discussed time permitting. (Joint work with Ruey Tsay, U of Chicago)