Testing variability in multivariate quality control: a conditional entropy measure approach
Information Sciences—Informatics and Computer Science: An International Journal
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Convex optimization techniques for fitting sparse Gaussian graphical models
ICML '06 Proceedings of the 23rd international conference on Machine learning
The Journal of Machine Learning Research
First-Order Methods for Sparse Covariance Selection
SIAM Journal on Matrix Analysis and Applications
Covariance structure regularization via entropy loss function
Computational Statistics & Data Analysis
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Multivariate control charts are essential tools in multivariate statistical process control. In real applications, when a multivariate process shifts, it occurs in either location or scale. Several methods have been proposed recently to monitor the covariance matrix. Most of these methods deal with a full rank covariance matrix, i.e., in a situation where the number of rational subgroups is larger than the number of variables. When the number of features is nearly as large as, or larger than, the number of observations, existing Shewhart-type charts do not provide a satisfactory solution because the estimated covariance matrix is singular. A new Shewhart-type chart for monitoring changes in the covariance matrix of a multivariate process when the number of observations available is less than the number of variables is proposed. This chart can be used to monitor the covariance matrix with only one observation. The new control chart is based on using the graphical LASSO estimator of the covariance matrix instead of the traditional sample covariance matrix. The LASSO estimator is used here because of desirable properties such as being non-singular and positive definite even when the number of observations is less than the number of variables. The performance of this new chart is compared to that of several Shewhart control charts for monitoring the covariance matrix.