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Volumn 4, Issue 1, 2005, Pages 1-30

A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics

Author keywords

"small n, large p" problem; Covariance estimation; Gene expression; Genetic network; Graphical Gaussian model (GGM); Shrinkage

Indexed keywords

ARTICLE; BIOINFORMATICS; CORRELATION ANALYSIS; COVARIANCE; DATA ANALYSIS; FUNCTIONAL GENOMICS; MATHEMATICAL ANALYSIS; POPULATION GENETICS; STATISTICAL ANALYSIS;

EID: 27844521293     PISSN: 15446115     EISSN: 15446115     Source Type: Journal    
DOI: 10.2202/1544-6115.1175     Document Type: Article
Times cited : (1277)

References (46)
  • 1
    • 0742305866 scopus 로고    scopus 로고
    • Network biology: Understanding the cell's functional organization
    • Barabási, A.-L. and Z. N. Oltvai (2004). Network biology: understanding the cell's functional organization. Nature Rev. Genetics 5, 101-113.
    • (2004) Nature Rev. Genetics , vol.5 , pp. 101-113
    • Barabási, A.-L.1    Oltvai, Z.N.2
  • 2
    • 0001677717 scopus 로고
    • Controlling the false discovery rate: A practical and powerful approach to multiple testing
    • Benjamini, Y. and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Statist. Soc. B 57, 289-300.
    • (1995) J. R. Statist. Soc. B , vol.57 , pp. 289-300
    • Benjamini, Y.1    Hochberg, Y.2
  • 4
    • 0034710924 scopus 로고    scopus 로고
    • Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks
    • Butte, A. J., P. Tamayo, D. Slonim, T. R. Golub, and I. S. Kohane (2000). Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. Proc. Natl. Acad. Sci. USA 97, 12182-12186.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 12182-12186
    • Butte, A.J.1    Tamayo, P.2    Slonim, D.3    Golub, T.R.4    Kohane, I.S.5
  • 5
    • 24144486294 scopus 로고    scopus 로고
    • A note on pseudolikelihood from marginal densities
    • Cox, D. R. and N. Reid (2004). A note on pseudolikelihood from marginal densities. Biometrika 91, 729-737.
    • (2004) Biometrika , vol.91 , pp. 729-737
    • Cox, D.R.1    Reid, N.2
  • 6
    • 24144445705 scopus 로고    scopus 로고
    • Improved statistical tests for differential gene expression by shrinking variance components estimates
    • Cui, X., J. T. G. Hwang, J. Qiu, N. J. Blades, and G. A. Churchill (2005). Improved statistical tests for differential gene expression by shrinking variance components estimates. Biostatistics 6, 59-75.
    • (2005) Biostatistics , vol.6 , pp. 59-75
    • Cui, X.1    Hwang, J.T.G.2    Qiu, J.3    Blades, N.J.4    Churchill, G.A.5
  • 7
    • 0035185654 scopus 로고    scopus 로고
    • Shrinkage estimators for covariance matrices
    • Daniels, M. J. and R. E. Kass (2001). Shrinkage estimators for covariance matrices. Biometrics 57, 1173-1184.
    • (2001) Biometrics , vol.57 , pp. 1173-1184
    • Daniels, M.J.1    Kass, R.E.2
  • 8
    • 12344321571 scopus 로고    scopus 로고
    • Discovery of meaningful associations in genomic data using partial correlation coefficients
    • de la Fuente, A., N. Bing, I. Hoeschele, and P. Mendes (2004). Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics 20, 3565-3574.
    • (2004) Bioinformatics , vol.20 , pp. 3565-3574
    • De La Fuente, A.1    Bing, N.2    Hoeschele, I.3    Mendes, P.4
  • 10
    • 0343784734 scopus 로고
    • Biased versus unbiased estimation
    • Efron, B. (1975). Biased versus unbiased estimation. Adv. Math. 16, 259-277.
    • (1975) Adv. Math. , vol.16 , pp. 259-277
    • Efron, B.1
  • 11
    • 0001768361 scopus 로고
    • Maximum likelihood and decision theory
    • Efron, B. (1982). Maximum likelihood and decision theory. Ann. Statist. 10, 340-356.
    • (1982) Ann. Statist. , vol.10 , pp. 340-356
    • Efron, B.1
  • 12
    • 2142732441 scopus 로고    scopus 로고
    • Large-scale simultaneous hypothesis testing: The choice of a null hypothesis
    • Efron, B. (2004). Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. J. Amer. Statist. Assoc. 99, 96-104.
    • (2004) J. Amer. Statist. Assoc. , vol.99 , pp. 96-104
    • Efron, B.1
  • 14
    • 27844581857 scopus 로고    scopus 로고
    • Preprint, Dept. of Statistics, Stanford University
    • Efron, B. (2005b). Local false discovery rates. Preprint, Dept. of Statistics, Stanford University.
    • (2005) Local False Discovery Rates
    • Efron, B.1
  • 15
    • 84949161141 scopus 로고
    • Data analysis using Stein's estimator and its generalizations
    • Efron, B. and C. N. Morris (1975). Data analysis using Stein's estimator and its generalizations. J. Amer. Statist. Assoc. 70, 311-319.
    • (1975) J. Amer. Statist. Assoc. , vol.70 , pp. 311-319
    • Efron, B.1    Morris, C.N.2
  • 16
    • 0000129805 scopus 로고
    • Stein's paradox in statistics
    • Efron, B. and C. N. Morris (1977). Stein's paradox in statistics. Sci. Am. 236, 119-127.
    • (1977) Sci. Am. , vol.236 , pp. 119-127
    • Efron, B.1    Morris, C.N.2
  • 18
    • 84887916087 scopus 로고
    • Regularized discriminant analysis
    • Friedman, J. H. (1989). Regularized discriminant analysis. J. Amer. Statist. Assoc. 84, 165-175.
    • (1989) J. Amer. Statist. Assoc. , vol.84 , pp. 165-175
    • Friedman, J.H.1
  • 19
    • 0033994631 scopus 로고    scopus 로고
    • Principles of multilevel modelling
    • Greenland, S. (2000). Principles of multilevel modelling. Intl. J. Epidemiol. 29, 158-167.
    • (2000) Intl. J. Epidemiol. , vol.29 , pp. 158-167
    • Greenland, S.1
  • 22
    • 0000379660 scopus 로고
    • Computing a nearest symmetric positive semidefinite matrix
    • Higham, N. J. (1988). Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 103, 103-118.
    • (1988) Linear Algebra Appl. , vol.103 , pp. 103-118
    • Higham, N.J.1
  • 24
    • 84942487147 scopus 로고
    • Ridge regression: Applications to nonorthogonal problems
    • Hoerl, A. E. and R. W. Kennard (1970a). Ridge regression: applications to nonorthogonal problems. Technometrics 12, 69-82.
    • (1970) Technometrics , vol.12 , pp. 69-82
    • Hoerl, A.E.1    Kennard, R.W.2
  • 25
    • 84942484786 scopus 로고
    • Ridge regression: Biased estimation for nonorthogonal problems
    • Hoerl, A. E. and R. W. Kennard (1970b). Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55-67.
    • (1970) Technometrics , vol.12 , pp. 55-67
    • Hoerl, A.E.1    Kennard, R.W.2
  • 26
    • 0000988073 scopus 로고
    • New light on the correlation coefficient and its transforms
    • Hotelling, H. (1953). New light on the correlation coefficient and its transforms. J. R. Statist. Soc. B 15, 193-232.
    • (1953) J. R. Statist. Soc. B , vol.15 , pp. 193-232
    • Hotelling, H.1
  • 27
    • 0041841552 scopus 로고    scopus 로고
    • Improved estimation of the covariance matrix of stock returns with an application to portfolio selection
    • Ledoit, O. and M. Wolf (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empir. Finance 10, 603-621.
    • (2003) J. Empir. Finance , vol.10 , pp. 603-621
    • Ledoit, O.1    Wolf, M.2
  • 28
    • 4344637588 scopus 로고    scopus 로고
    • Honey, I shrunk the sample covariance matrix
    • Ledoit, O. and M. Wolf (2004a). Honey, I shrunk the sample covariance matrix. J. Portfolio Management 30, 110-119.
    • (2004) J. Portfolio Management , vol.30 , pp. 110-119
    • Ledoit, O.1    Wolf, M.2
  • 29
    • 0346961488 scopus 로고    scopus 로고
    • A well conditioned estimator for large-dimensional covariance matrices
    • Ledoit, O. and M. Wolf (2004b). A well conditioned estimator for large-dimensional covariance matrices. J. Multiv. Anal. 88, 365-411.
    • (2004) J. Multiv. Anal. , vol.88 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 30
    • 7844236774 scopus 로고    scopus 로고
    • Estimation of the scale matrix and its eigen-values in the Wishart and the multivariate F distributions
    • Leung, P. L. and W. Y. Chan (1998). Estimation of the scale matrix and its eigen-values in the Wishart and the multivariate F distributions. Ann. Inst. Statist. Math. 50, 523-530.
    • (1998) Ann. Inst. Statist. Math. , vol.50 , pp. 523-530
    • Leung, P.L.1    Chan, W.Y.2
  • 31
    • 27844482652 scopus 로고    scopus 로고
    • Estimating genomic coexpression networks using first-order conditional independence
    • Magwene, P. M. and J. Kim (2004). Estimating genomic coexpression networks using first-order conditional independence. Genome Biology 5, R100.
    • (2004) Genome Biology , vol.5
    • Magwene, P.M.1    Kim, J.2
  • 33
    • 27844457733 scopus 로고    scopus 로고
    • High dimensional graphs and variable selection with the lasso
    • in press
    • Meinshausen, N. and P. Bühlmann (2005). High dimensional graphs and variable selection with the lasso. Ann. Statist. in press.
    • (2005) Ann. Statist.
    • Meinshausen, N.1    Bühlmann, P.2
  • 34
    • 84950432453 scopus 로고
    • Parametric empirical Bayes inference: Theory and applications
    • Morris, C. N. (1983). Parametric empirical Bayes inference: theory and applications. J. Amer. Statist. Assoc. 78, 47-55.
    • (1983) J. Amer. Statist. Assoc. , vol.78 , pp. 47-55
    • Morris, C.N.1
  • 35
    • 15944364151 scopus 로고    scopus 로고
    • An empirical Bayes approach to inferring large-scale gene association networks
    • Schäfer, J. and K. Strimmer (2005a). An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics 21, 754-764.
    • (2005) Bioinformatics , vol.21 , pp. 754-764
    • Schäfer, J.1    Strimmer, K.2
  • 36
    • 33749479885 scopus 로고    scopus 로고
    • Learning large-scale graphical Gaussian models from genomic data
    • J. F. F. Mendes, S. N. Dorogovtsev, A. Povolotsky, F. V. Abreu, and J. G. Oliveira (Eds.), AIP Conference Proceedings, Aveiro, PT, August 2004, American Institute of Physics
    • Schäfer, J. and K. Strimmer (2005b). Learning large-scale graphical Gaussian models from genomic data. In J. F. F. Mendes, S. N. Dorogovtsev, A. Povolotsky, F. V. Abreu, and J. G. Oliveira (Eds.), Science of Complex Networks: From Biology to the Internet and WWW, Volume 776, AIP Conference Proceedings, Aveiro, PT, August 2004, pp. 263-276. American Institute of Physics.
    • (2005) Science of Complex Networks: From Biology to the Internet and WWW , vol.776 , pp. 263-276
    • Schäfer, J.1    Strimmer, K.2
  • 37
    • 17444378513 scopus 로고    scopus 로고
    • Reverse engineering of the stress response during expression of a recombinant protein
    • 10-12 June 2004, Aachen, Germany, Verlag Mainz
    • Schmidt-Heck, W., R. Guthke, S. Toepfer, H. Reischer, K. Duerrschmid, and K. Bayer (2004). Reverse engineering of the stress response during expression of a recombinant protein. In Proceedings of the EUNITE symposium, 10-12 June 2004, Aachen, Germany, pp. 407-412. Verlag Mainz.
    • (2004) Proceedings of the EUNITE Symposium , pp. 407-412
    • Schmidt-Heck, W.1    Guthke, R.2    Toepfer, S.3    Reischer, H.4    Duerrschmid, K.5    Bayer, K.6
  • 38
    • 4544341015 scopus 로고    scopus 로고
    • Linear models and empirical Bayes methods for assessing differential expression in microarray experiments
    • Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statist. Appl. Genet. Mol. Biol. 3, 3.
    • (2004) Statist. Appl. Genet. Mol. Biol. , vol.3 , pp. 3
    • Smyth, G.K.1
  • 39
    • 0000813561 scopus 로고
    • Inadmissibility of the usual estimator for the mean of a multivariate distribution
    • J. Neyman (Ed.), Berkeley, Univ. California Press
    • Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate distribution. In J. Neyman (Ed.), Proc. Third. Berkeley Symp. Math. Statist. Probab., Volume 1, Berkeley, pp. 197-206. Univ. California Press.
    • (1956) Proc. Third. Berkeley Symp. Math. Statist. Probab. , vol.1 , pp. 197-206
    • Stein, C.1
  • 40
    • 0036020892 scopus 로고    scopus 로고
    • A direct approach to false discovery rates
    • Storey, J. D. (2002). A direct approach to false discovery rates. J. R. Statist. Soc. B 64, 479-498.
    • (2002) J. R. Statist. Soc. B , vol.64 , pp. 479-498
    • Storey, J.D.1
  • 41
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B 58, 267-288.
    • (1996) J. R. Statist. Soc. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 42
    • 0037076272 scopus 로고    scopus 로고
    • Diagnosis of multiple cancer type by shrunken centroids of gene expression
    • Tibshirani, R., T. Hastie, B. Narasimhan, and G. Chi (2002). Diagnosis of multiple cancer type by shrunken centroids of gene expression. Proc. Natl. Acad. Sci. USA 99, 6567-6572.
    • (2002) Proc. Natl. Acad. Sci. USA , vol.99 , pp. 6567-6572
    • Tibshirani, R.1    Hastie, T.2    Narasimhan, B.3    Chi, G.4
  • 43
    • 0036191190 scopus 로고    scopus 로고
    • Inference of a genetic network by a combined approach of cluster analysis and graphical Gaussian modeling
    • Toh, H. and K. Horimoto (2002). Inference of a genetic network by a combined approach of cluster analysis and graphical Gaussian modeling. Bioinformatics 18, 287-297.
    • (2002) Bioinformatics , vol.18 , pp. 287-297
    • Toh, H.1    Horimoto, K.2
  • 46
    • 15944363312 scopus 로고    scopus 로고
    • Classification of gene microarrays by penalized logistic regression
    • Zhu, J. and T. Hastie (2004). Classification of gene microarrays by penalized logistic regression. Biostatistics 5, 427-443.
    • (2004) Biostatistics , vol.5 , pp. 427-443
    • Zhu, J.1    Hastie, T.2


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