A0627
Title: Estimation of multiple large covariance matrices and its application to high-dimensional quadratic discriminant analysis
Authors: Yingli Qin - University of Waterloo (Canada) [presenting]
Mu Zhu - University of Waterloo (Canada)
Liyuan Zheng - University of Waterloo (Canada)
Yilei Wu - University of Waterloo (Canada)
Weiming Li - Shanghai University of Finance and Economics (China)
Abstract: When estimating covariance matrices for data from multiple related categories, such as different subtypes of a particular disease, it is possible that these covariance matrices may exhibit shared structural components. The precision matrix (the inverse of the covariance matrix) of each category is assumed to be decomposed into a common diagonal component, a common low-rank component and a category-specific low-rank component. This decomposition can be motivated by a factor model, in which the effects of some latent factors are common across all categories while others are specific to individual categories. A method to jointly estimate these precision matrices is proposed, thereby inferring the covariance matrices as well, starting with an estimation of the number of factors. The approach incorporates a complexity penalty to promote the imposition of low-rank structures. Under moderate conditions, The consistency of the estimators is established. Furthermore, these estimators are applied to formulate a high-dimensional quadratic discriminant analysis rule. Its convergence rate is established for the classification error. Finally, the method is illustrated through numerical examples.
