Detecting the Dimensionality for Principal Components Model

References

• Auer , P. , Gervini , D. ( 2008 ). Choosing principal components: a new graphical method based on Bayesian model selection . Communication in Statistics – Simulation and Computation 37 : 962 – 977 .
   Web of Science ®Google Scholar
• Casella , G. , Moreno , E. ( 2006 ). Objective Bayesian variable selection . Journal of the American Statistical Association 101 : 157 – 167 .
   Web of Science ®Google Scholar
• Cattell , R. B. ( 1966 ). The scree test for the number of factors . Multivariate Behavorial Research 1 : 245 – 276 .
   PubMed Web of Science ®Google Scholar
• Dempster , A. P. , Laird , N. M. , Rubin , D. B. ( 1977 ). Maximum likelihood from incomplete data via the EM algorithm (with discussion) . Journal of the Royal Statistical Society, Series B 39 : 1 – 38 .
   Google Scholar
• Everson , R. , Roberts , S. ( 2000 ). Inferring the eigenvalues of covariance matrix from limited noisy data . IEEE Transactions on Signal Processing 48 : 2083 – 2091 .
   Web of Science ®Google Scholar
• Fan , J. , Li , R. ( 2001 ). Variable selection via nonconcave penelized likelihood and its oracle properties . Journal of the American Statistical Association 96 : 1348 – 1360 .
   Web of Science ®Google Scholar
• George , E. I. , McCulloch , R. E. ( 1993 ). Variable selection via Gibbs samplng . Journal of the American Statisticial Association 88 : 881 – 889 .
   Web of Science ®Google Scholar
• George , E. I. , McCulloch , R. E. ( 1997 ). Approaches for Bayesian variable selection . Statistica Sinica 7 : 339 – 373 .
   Web of Science ®Google Scholar
• Huang , J. , Liu , N. , Pourahmadi , M. , Liu , L. ( 2006 ). Covariance matrix selection and estimation via penalised normal likelihood . Biometrika 93 : 85 – 98 .
   Web of Science ®Google Scholar
• Kass , R. E. , Raftery , A. E. ( 1995 ). Bayes factors . Journal of the American Statisticial Association 90 : 773 – 795 .
   Web of Science ®Google Scholar
• Levina , E. , Rothman , A. , Zhu , J. ( 2008 ). Sparse estimation of large covariance matrices via a nested LASSO penalty . The Annals of Applied Statistics 2 : 245 – 263 .
   Web of Science ®Google Scholar
• Meng , X.-L. , Rubin , D. B. ( 1993 ). Mazimum likelihood estimation via the ECM algorithm: A general framework . Biometrika 80 : 267 – 278 .
   Web of Science ®Google Scholar
• Minka , T. P. ( 2001 ). Automatic choice of dimensionality for PCA . Advances in Neural Information Processing System 13 : 598 – 604 .
   Google Scholar
• Rajan , J. J. , Rayner , P. J. W. (1997). Model order selection for the singular value decomposition and the discrete Karhmen–Loeve transform using a Bayesian approach. IEE Vision, Image and Signal Processing 144:166–123.
   Google Scholar
• Seber , G. A. F. ( 1984 ). Multivariate Observations . New York : Wiley .
   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
• Tipping , M. E. , Bishop , C. M. ( 1999 ). Probabilistic principal components analysis . Journal of the Royal Statistical Society, Series B 61 : 611 – 622 .
   Web of Science ®Google Scholar
• Tsay , R. S. ( 2005 ). Analysis of Financial Time Series. , 2nd ed. New Jersey : John Wiley & Sons .
   Google Scholar
• Wold , S. ( 1978 ). Cross validatory estimation of the components in factor and principal component models . Technometrics 20 : 397 – 405 .
   Web of Science ®Google Scholar
• Zhang , Z. , Chan , K. L. , Kwok , J. T. , Yeung , D. Y. ( 2004 ). Bayesian inference on principal component analysis using reversible jump Markov chain Monte Carlo . In Proceedings of Nineteenth National Conference on Artificial Intelligence (AAAI'04) San Jose , CA , July 25–29 , pp. 372 – 377 .
   Google Scholar
• Zou , H. ( 2006 ). The adaptive LASSO and its oracle properties . Journal of the American Statistical Association 101 : 1418 – 1429 .
   Web of Science ®Google Scholar