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Title: Joint estimation of covariance matrix via Cholesky Decomposition
Keywords: Covariance Matrix, Sparsity, Group LASSO, Penalty Function, Longitudinal Data
Issue Date: 15-Aug-2012
Citation: JIANG XIAOJUN (2012-08-15). Joint estimation of covariance matrix via Cholesky Decomposition. ScholarBank@NUS Repository.
Abstract: In this research, we focus on jointly estimating covariance matrix and precision matrix for grouped data with natural order via Cholesky decomposition. We treat autoregressive parameters at the same position in different groups as a set and impose penalty functions with group effect to these parameters together. Sparse sup-norm penalty and sparse group LASSO penalty are used in our methods. When data structures in different groups are close, our approaches can do better than separate estimation approaches by providing more accurate covariance and precision matrix estimates and they are guaranteed to be positive definite. Coordinate decent algorithm is used in the optimization procedure and consistent rates of our estimator have been established in this study. In the simulation part, we show their good performance by comparing our methods with the separated estimation methods. An application to classify cattle from two treatment groups based on their weights is also included.
Appears in Collections:Ph.D Theses (Open)

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