Title
Monitoring the covariance matrix with fewer observations than variables
Abbreviated Journal Title
Comput. Stat. Data Anal.
Keywords
Covariance matrix; Penalized likelihood function; Average run length; (ARL); Multistandardization; Cholesky decomposition; INDIVIDUAL OBSERVATIONS; PROCESS VARIABILITY; SELECTION; LIKELIHOOD; LASSO; MODEL; Computer Science, Interdisciplinary Applications; Statistics &; Probability
Abstract
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. (c) 2013 Elsevier B.V. All rights reserved.
Journal Title
Computational Statistics & Data Analysis
Volume
64
Publication Date
1-1-2013
Document Type
Article
Language
English
First Page
99
Last Page
112
WOS Identifier
ISSN
0167-9473
Recommended Citation
"Monitoring the covariance matrix with fewer observations than variables" (2013). Faculty Bibliography 2010s. 4356.
https://stars.library.ucf.edu/facultybib2010/4356
Comments
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