Adaptive Block Banding Precision Matrix Estimation For Multivariate Longitudinal Data

We propose an estimator for precision matrices with the structure of Banded Kronecker Sparse forms (BKS).BKS takes advantage of the special feature of a precision matrix, which has the form of the kronecker product of an adaptively banded matrix and a sparse matrix, both are positive definite.Such precision matrix arises frequently in practice in finance data, medical data and time series data.We achieve the adaptive bandedness via a specially designed penalty, and enforce the sparsity via lasso.We apply a computationally efficient procedure named Alternative Convex Search (ACS) algorithm to implement BKS.We establish the computational convergence and show the statistical guarantee through establishing the asymptotic rate.Our extensive simulation studies indicate the superior finite sample performance of BKS in comparison to existing methods.Additionally, we apply BKS to EEG and ADHD datasets, wherein it outperforms other methods in capturing the banding sparsity characteristics of the precision matrix.