Monitoring the covariance matrix via penalized likelihood estimation

References

• Alt , F. 1984 . “ Multivariate quality control ” . In Encyclopedia of Statistical Sciences Vol. 6 , 110 – 122 .
   Google Scholar
• Alt , F. B. and Bedewi , G. E. 1986 . SPC for dispersion for multivariate data . ASQC Quality Congress Transactions , : 248 – 254 .
   Google Scholar
• Alt , F. B. and Smith , N. D. 1988 . “ Multivariate process control ” . In Handbook of Statistics , Edited by: Krishnaiah , P.R. and Rao , C.R. 333 – 351 . New York , NY : Elsevier Science Publishers .
   Google Scholar
• Chen , A. and Hong , H.-J. 2010 . “ Fault detection and classification by sample covariance matrix and its application to plasma etcher ” . Taiwan : Preprint, National Taiwan University .
   Google Scholar
• D’Aspremont , A. , Banerjee , O. and El Ghaoui , L. 2008 . First-order methods for sparse covariance selection . Siam Journal on Matrix Analysis and Applications , 30 : 56 – 66 .
   Web of Science ®Google Scholar
• Dempster , A. 1972 . Covariance selection . Biometrics , 28 : 157 – 175 .
   Web of Science ®Google Scholar
• Friedman , J. , Hastie , T. and Tibshirani , R. 2008 . Sparse inverse covariance estimation with the graphical LASSO . Biostatistics , 9 : 432 – 441 .
   PubMed Web of Science ®Google Scholar
• Guerrero-Cusumano , J. L. 1995 . Testing variability in multivariate quality control—a conditional entropy measure approach . Information Sciences , 86 : 179 – 202 .
   Web of Science ®Google Scholar
• Hawkins , D. M. 1991 . Multivariate quality control based on regression adjusted variables . Technometrics , 33 : 61 – 75 .
   Web of Science ®Google Scholar
• Hawkins , D. M. and Maboudou-Tchao , E. M. 2008 . Multivariate exponentially weighted moving covariance matrix . Technometrics , 50 : 155 – 166 .
   Web of Science ®Google Scholar
• Healy , J. D. 1987 . A note on multivariate CUSUM procedures . Technometrics , 29 : 409 – 412 .
   Web of Science ®Google Scholar
• Hotelling , H. 1947 . “ Multivariate quality control-illustrated by the air testing of sample bombsights ” . In Techniques of Statistical Analysis , Edited by: Eisenhart , C. , Wallis , M.W. and Hastay , W.A. 111 – 184 . New York , NY : McGraw-Hill .
   Google Scholar
• Huang , J. Z. , Liu , N. P. , Pourahmadi , M. and Liu , L. X. 2006 . Covariance matrix selection and estimation via penalised normal likelihood . Biometrika , 93 : 85 – 98 .
   Web of Science ®Google Scholar
• Huwang , L. , Yeh , A. B. and Wu , C.-W . 2007 . Monitoring multivariate process variability with individual observations . Journal of Quality Technology , 39 : 258 – 278 .
   Web of Science ®Google Scholar
• O’Mara , W. , Herring , R. and Hunt , L. 2007 . Handbook of Semiconductor Silicon Technology , South Africa : Crest Publishing House .
   Google Scholar
• Pourahmadi , M. 1999 . Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation . Biometrika , 86 : 677 – 690 .
   Web of Science ®Google Scholar
• Pourahmadi , M. 2000 . Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix . Biometrika , 87 : 425 – 435 .
   Web of Science ®Google Scholar
• Reynolds , R. M. Jr and G.-Y , Cho . 2006 . Multivariate control charts for monitoring the mean vector and covariance matrix . Journal of Quality Technology , 38 : 230 – 253 .
   Web of Science ®Google Scholar
• Rothman , A. J. , Bickel , P. J. , Levina , E. and Zhu , J. 2008 . Sparse permutation invariant covariance estimation . Electronic Journal of Statistics , 2 : 494 – 515 .
   Web of Science ®Google Scholar
• Rothman , A. J. , Levina , E. and Zhu , J. 2010 . Sparse multivariate regression with covariance estimation . Journal of Computational and Graphical Statistics , 19 : 947 – 962 .
   PubMed Web of Science ®Google Scholar
• Stoumbos , Z. G. , Reynolds , M. R. , Ryan , T.P. Jr and Woodall , W. H. 2000 . The state of statistical process control as we proceed into the 21st century . Journal of the American Statistical Association , 95 : 992 – 998 .
   Web of Science ®Google Scholar
• Tang , P. F. and Barnett , N. S. 1996a . Dispersion control for multivariate processes . Australian Journal of Statistics , 38 : 235 – 251 .
   Google Scholar
• Tang , P. F. and Barnett , N. S. 1996b . Dispersion control for multivariate processes—some comparisons . Australian Journal of Statistics , 38 : 253 – 273 .
   Google Scholar
• Tibshirani , R. 1996 . Regression shrinkage and selection via the LASSO . Journal of the Royal Statistical Society, Series B , 58 : 267 – 288 .
   Google Scholar
• Wang , K. and Jiang , W. 2009 . High-dimensional process monitoring and fault isolation via variable selection . Journal of Quality Technology , 41 : 247 – 258 .
   Web of Science ®Google Scholar
• Williams , J. , Woodall , W. , Birch , J. and Sullivan , J. 2006 . On the distribution of Hotelling’s T 2 statistic based on the successive differences covariance matrix estimator . Journal of Quality Technology , 38 : 217 – 229 .
   Web of Science ®Google Scholar
• Witten , D. M. and Tibshirani , R. 2009 . Covariance-regularized regression and classification for high dimensional problems . Journal of the Royal Statistical Society, Series B , 69 : 329 – 346 .
   Google Scholar
• Woodall , W. H. 2000 . Controversies and contradictions in statistical process control (with discussions) . Journal of Quality Control , 32 : 341 – 378 .
   Google Scholar
• Woodall , W. H. and Montgomery , D. C. 1999 . Research issues and ideas in statistical process control . Journal of Quality Technology , 31 : 376 – 386 .
   Web of Science ®Google Scholar
• Yeh , A. B. , Huwang , L. and Wu , C. W. 2005 . A multivariate EWMA control chart for monitoring process variability with individual observations . IIE Transactions on Quality and Reliability Engineering , 37 : 1023 – 1035 .
   Web of Science ®Google Scholar
• Yeh , A. B. , Huwang , L. C. and Wu , Y. F. 2004 . A likelihood-ratio based EWMA control chart for monitoring variability of multivariate normal processes . IIE Transactions on Quality and Reliability Engineering , 36 : 865 – 879 .
   Web of Science ®Google Scholar
• Yeh , A. B. , Lin , D. and McGrath , R. 2006 . Multivariate control charts for monitoring covariance matrix: a review . Quality Technology and Quantitative Management , 3 : 415 – 436 .
   Google Scholar
• Yen , C. and Shiau , J.J.H . 2010 . A multivariate control chart for detecting increases in process dispersion . Statistica Sinica , 20 : 1683 – 1707 .
   Web of Science ®Google Scholar
• Yuan , M. and Lin , Y. 2007 . Model selection and estimation in the Gaussian graphical model . Biometrika , 94 : 19 – 35 .
   Web of Science ®Google Scholar
• Zhang , J. , Li , Z. and Wang , Z. 2009 . Multivariate control chart for simultaneously monitoring process mean and variability . Computational Statistics & Data Analysis , 54 : 2244 – 2252 .
   Web of Science ®Google Scholar
• Zou , C. , Ning , X. and Tsung , F. 2010 . LASSO-based multivariate linear profile monitoring . Annals of Operations Research , 192 : 3 – 19 .
   Web of Science ®Google Scholar
• Zou , C. and Qiu , P. 2009 . Multivariate statistical process control using LASSO . Journal of The American Statistical Association , 104 : 1586 – 1596 .
   Web of Science ®Google Scholar