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Volumn 185, Issue 3, 2010, Pages 1097-1110

Better estimates of genetic covariance matrices by "bending" using penalized maximum likelihood

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ARTICLE; BEEF CATTLE; CENTRAL TENDENCY BIAS; GENETIC CORRELATION; GENETIC COVARIANCE MATRIX; GENETIC VARIABILITY; HERITABILITY; MAXIMUM LIKELIHOOD METHOD; NONHUMAN; PHENOTYPIC COVARIANCE MATRIX; PRIORITY JOURNAL; QUANTITATIVE GENETICS; SAMPLE SIZE; SAMPLING ERROR; ANALYSIS OF VARIANCE; ANIMAL; BIOLOGICAL MODEL; CATTLE; COMPUTER SIMULATION; FEMALE; MALE; STATISTICAL MODEL;

EID: 78349236236     PISSN: 00166731     EISSN: 00166731     Source Type: Journal    
DOI: 10.1534/genetics.109.113381     Document Type: Article
Times cited : (24)

References (62)
  • 1
    • 0000513344 scopus 로고
    • What should be done when an estimated between-group covariance matrix is not nonnegative definite?
    • AMEMIYA, Y., 1985 What should be done when an estimated between-group covariance matrix is not nonnegative definite? Am. Stat. 39: 112-117.
    • (1985) Am. Stat. , vol.39 , pp. 112-117
    • Amemiya, Y.1
  • 2
    • 0000687468 scopus 로고
    • Maximum likelihood estimators and likelihood ratio criteria in multivariate components of variance
    • ANDERSON, B. M., T. W. ANDERSON and I. OLKIN, 1986 Maximum likelihood estimators and likelihood ratio criteria in multivariate components of variance. Ann. Stat. 14: 405-417.
    • (1986) Ann. Stat. , vol.14 , pp. 405-417
    • Anderson, B.M.1    Anderson, T.W.2    Olkin, I.3
  • 4
    • 0010869555 scopus 로고
    • Exact probabilities of obtaining estimated non-positive definite between-group covariance matrices
    • BHARGAVA, A. K., and D. DISCH, 1982 Exact probabilities of obtaining estimated non-positive definite between-group covariance matrices. J. Stat. Comp. Simul. 15: 27-32.
    • (1982) J. Stat. Comp. Simul. , vol.15 , pp. 27-32
    • Bhargava, A.K.1    Disch, D.2
  • 5
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • BICKEL, P. J., and E. LEVINA, 2008 Regularized estimation of large covariance matrices. Ann. Stat. 36: 199-227.
    • (2008) Ann. Stat. , vol.36 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 6
    • 33845678003 scopus 로고    scopus 로고
    • Regularization in statistics
    • BICKEL, P. J., and B. LI, 2006 Regularization in statistics. Test 15: 271-303.
    • (2006) Test , vol.15 , pp. 271-303
    • Bickel, P.J.1    Li, B.2
  • 8
    • 0011837693 scopus 로고
    • Estimates of direct and maternal genetic correlations for pupa weight and family size of Tribolium
    • BONDARI, K., R. L. WILLHAM and A. E. FREEMAN, 1978 Estimates of direct and maternal genetic correlations for pupa weight and family size of Tribolium. J. Anim. Sci. 47: 358-365.
    • (1978) J. Anim. Sci. , vol.47 , pp. 358-365
    • Bondari, K.1    Willham, R.L.2    Freeman, A.E.3
  • 9
    • 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
  • 10
    • 0001038826 scopus 로고
    • Covariance selection
    • DEMPSTER, A. P., 1972 Covariance selection. Biometrics 28: 157-175.
    • (1972) Biometrics , vol.28 , pp. 157-175
    • Dempster, A.P.1
  • 11
    • 0000752425 scopus 로고
    • Estimation of a covariance matrix under Stein's loss
    • DEY, D., and C. SRINIVASAN, 1985 Estimation of a covariance matrix under Stein's loss. Ann. Stat. 13: 1581-1591.
    • (1985) Ann. Stat. , vol.13 , pp. 1581-1591
    • Dey, D.1    Srinivasan, C.2
  • 12
    • 62249113520 scopus 로고    scopus 로고
    • Estimation, prediction and inference for the LASSO random effects model
    • FOSTER, S. D., A. P. VERBYLA and W. S. PITCHFORD, 2009 Estimation, prediction and inference for the LASSO random effects model. Aust. N Z J. Stat. 51: 43-61.
    • (2009) Aust. N Z J. Stat. , vol.51 , pp. 43-61
    • Foster, S.D.1    Verbyla, A.P.2    Pitchford, W.S.3
  • 13
    • 84952149204 scopus 로고
    • A statistical view of some chemometrics regression tools
    • FRANK, I. E., and J. H. FRIEDMAN, 1993 A statistical view of some chemometrics regression tools. Technometrics 35: 109-135.
    • (1993) Technometrics , vol.35 , pp. 109-135
    • Frank, I.E.1    Friedman, J.H.2
  • 14
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • FRIEDMAN, J., T. HASTIE and R. TIBSHIRANI, 2008 Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9: 432-441.
    • (2008) Biostatistics , vol.9 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 15
    • 0003289477 scopus 로고    scopus 로고
    • Penalized likelihood
    • John Wiley & Sons, New York
    • GREEN, P. J., 1998 Penalized likelihood, pp. 578-586 in Encyclopedia of Statistical Sciences, Vol. 2. John Wiley & Sons, New York.
    • (1998) Encyclopedia of Statistical Sciences , vol.2 , pp. 578-586
    • Green, P.J.1
  • 16
    • 0000406169 scopus 로고
    • Empirical Bayes estimation of the multivariate normal covariance matrix
    • HAFF, L. R., 1980 Empirical Bayes estimation of the multivariate normal covariance matrix. Ann. Stat. 8: 586-597.
    • (1980) Ann. Stat. , vol.8 , pp. 586-597
    • Haff, L.R.1
  • 17
    • 84890913931 scopus 로고
    • Maximum likelihood approaches to variance component estimation and related problems
    • HARVILLE, D. A., 1977 Maximum likelihood approaches to variance component estimation and related problems. J. Am. Stat. Assoc. 72: 320-338.
    • (1977) J. Am. Stat. Assoc. , vol.72 , pp. 320-338
    • Harville, D.A.1
  • 19
    • 0000819999 scopus 로고
    • Modifications of estimates of parameters in the construction of genetic selection indices ('bending')
    • HAYES, J. F., and W. G. HILL, 1981 Modifications of estimates of parameters in the construction of genetic selection indices ('bending'). Biometrics 37: 483-493.
    • (1981) Biometrics , vol.37 , pp. 483-493
    • Hayes, J.F.1    Hill, W.G.2
  • 20
    • 0018084894 scopus 로고
    • Probabilities of non-positive definite between-group or genetic covariance matrices
    • HILL, W. G., and R. THOMPSON, 1978 Probabilities of non-positive definite between-group or genetic covariance matrices. Biometrics 34: 429-439.
    • (1978) Biometrics , vol.34 , pp. 429-439
    • Hill, W.G.1    Thompson, R.2
  • 21
    • 84942487147 scopus 로고
    • Ridge regression: Applications to nonorthogonal problems
    • HOERL, A. E., and R. W. KENNARD, 1970 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
  • 22
    • 0348237092 scopus 로고    scopus 로고
    • Stein estimation - A review
    • HOFFMANN, K., 2000 Stein estimation - a review. Stat. Papers 41: 127-158.
    • (2000) Stat. Papers , vol.41 , pp. 127-158
    • Hoffmann, K.1
  • 23
    • 33644986127 scopus 로고    scopus 로고
    • Covariance matrix selection and estimation via penalised normal likelihood
    • HUANG, J. Z., N. LIU, M. POURAHMADI and L. LIU, 2006 Covariance matrix selection and estimation via penalised normal likelihood. Biometrika 93: 85-98.
    • (2006) Biometrika , vol.93 , pp. 85-98
    • Huang, J.Z.1    Liu, N.2    Pourahmadi, M.3    Liu, L.4
  • 25
    • 65649116390 scopus 로고    scopus 로고
    • Patterns of quantitative genetic variation in multiple dimensions
    • KIRKPATRICK, M., 2009 Patterns of quantitative genetic variation in multiple dimensions. Genetica 136: 271-284.
    • (2009) Genetica , vol.136 , pp. 271-284
    • Kirkpatrick, M.1
  • 26
    • 11244319412 scopus 로고    scopus 로고
    • Direct estimation of genetic principal components: Simplified analysis of complex phenotypes
    • KIRKPATRICK, M., and K. MEYER, 2004 Direct estimation of genetic principal components: simplified analysis of complex phenotypes. Genetics 168: 2295-2306.
    • (2004) Genetics , vol.168 , pp. 2295-2306
    • Kirkpatrick, M.1    Meyer, K.2
  • 27
    • 0025231585 scopus 로고
    • Analysis of the inheritance, selection and evolution of growth trajectories
    • KIRKPATRICK, M., D. LOFSVOLD and M. BULMER, 1990 Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124: 979-993.
    • (1990) Genetics , vol.124 , pp. 979-993
    • Kirkpatrick, M.1    Lofsvold, D.2    Bulmer, M.3
  • 28
    • 0009289555 scopus 로고
    • Maximum likelihood estimation of multivariate covariance components for the balanced one-way layout
    • KLOTZ, J., and J. PUTTER, 1969 Maximum likelihood estimation of multivariate covariance components for the balanced one-way layout. Ann. Math. Stat. 40: 1100-1105.
    • (1969) Ann. Math. Stat. , vol.40 , pp. 1100-1105
    • Klotz, J.1    Putter, J.2
  • 29
    • 58549098760 scopus 로고    scopus 로고
    • New answers for old questions: The evolutionary quantitative genetics of wild animal populations
    • KRUUK, L. E. B., J. SLATE and A. J. WILSON, 2008 New answers for old questions: the evolutionary quantitative genetics of wild animal populations. Annu. Rev. Ecol. Evol. Syst. 39: 525-548.
    • (2008) Annu. Rev. Ecol. Evol. Syst. , vol.39 , pp. 525-548
    • Kruuk, L.E.B.1    Slate, J.2    Wilson, A.J.3
  • 30
    • 0009884521 scopus 로고    scopus 로고
    • Shrinkage and modification techniques in estimation of variance and the related problems: A review
    • KUBOKAWA, T., 1999 Shrinkage and modification techniques in estimation of variance and the related problems: a review. Commun. Stat. Theory Methods 28: 613-650.
    • (1999) Commun. Stat. Theory Methods , vol.28 , pp. 613-650
    • Kubokawa, T.1
  • 31
    • 33749127473 scopus 로고    scopus 로고
    • Estimation of covariance matrices in fixed and mixed effects linear models
    • KUBOKAWA, T., and M. T. TSAI, 2006 Estimation of covariance matrices in fixed and mixed effects linear models. J. Multivar. Anal. 97: 2242-2261.
    • (2006) J. Multivar. Anal. , vol.97 , pp. 2242-2261
    • Kubokawa, T.1    Tsai, M.T.2
  • 32
    • 0000815369 scopus 로고
    • Tests of significance for the latent roots of covariance and correlation matrices
    • LAWLEY, D. N., 1956 Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43: 128-136.
    • (1956) Biometrika , vol.43 , pp. 128-136
    • Lawley, D.N.1
  • 33
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • LEDOIT, O., and M. WOLF, 2004 A well-conditioned estimator for large-dimensional covariance matrices. J. Multivar. Anal. 88: 365-411.
    • (2004) J. Multivar. Anal. , vol.88 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 34
    • 62349114549 scopus 로고    scopus 로고
    • Sparse estimation of large covariance matrices via a nested Lasso penalty
    • LEVINA, E., A. J. ROTHMAN and J. ZHU, 2008 Sparse estimation of large covariance matrices via a nested Lasso penalty. Ann. Appl. Stat. 2: 245-263.
    • (2008) Ann. Appl. Stat. , vol.2 , pp. 245-263
    • Levina, E.1    Rothman, A.J.2    Zhu, J.3
  • 35
    • 0000396393 scopus 로고
    • A Monte Carlo comparison of four estimators of a covariance matrix
    • edited by P. R. KRISHNAISH. North-Holland, Amsterdam
    • LIN, S. P., and M. D. PERLMAN, 1985 A Monte Carlo comparison of four estimators of a covariance matrix, pp. 411-428 in Multivariate Analysis, Vol. 6, edited by P. R. KRISHNAISH. North-Holland, Amsterdam.
    • (1985) Multivariate Analysis , vol.6 , pp. 411-428
    • Lin, S.P.1    Perlman, M.D.2
  • 36
    • 0010865655 scopus 로고
    • Estimating covariance matrices
    • LOH, W. L., 1991 Estimating covariance matrices. Ann. Stat. 19: 283-296.
    • (1991) Ann. Stat. , vol.19 , pp. 283-296
    • Loh, W.L.1
  • 37
    • 0009155159 scopus 로고
    • Improved nonnegative estimation of variance components in balanced multivariate mixed models
    • MATHEW, T., A. NIYOGI and B. K. SINHA, 1994 Improved nonnegative estimation of variance components in balanced multivariate mixed models. J. Multivar. Anal. 51: 83-101.
    • (1994) J. Multivar. Anal. , vol.51 , pp. 83-101
    • Mathew, T.1    Niyogi, A.2    Sinha, B.K.3
  • 38
    • 78651227721 scopus 로고    scopus 로고
    • Who cares if it is a white cat or a black cat? Discussion: "One-step sparse estimates in nonconcave penalized likelihood models"
    • MENG, X. L., 2008 Who cares if it is a white cat or a black cat? Discussion: "One-step sparse estimates in nonconcave penalized likelihood models" [Ann. Statist. 36 (2008), 1509-1533]
    • (2008) Ann. Statist. , vol.36 , Issue.2008 , pp. 1509-1533
    • Meng, X.L.1
  • 40
    • 77949844022 scopus 로고    scopus 로고
    • Factor-analytic models for genotype x environment type problems and structured covariance matrices
    • MEYER, K., 2009 Factor-analytic models for genotype x environment type problems and structured covariance matrices. Genet. Sel. Evol. 41: 21.
    • (2009) Genet. Sel. Evol. , vol.41 , pp. 21
    • Meyer, K.1
  • 41
    • 0005033851 scopus 로고
    • A note on the effects of sampling errors on the accuracy of genetic selection indices
    • MEYER, K., and W. G. HILL, 1983 A note on the effects of sampling errors on the accuracy of genetic selection indices. Z Tierzuecht Zuechtungsbiol. 100: 27-32.
    • (1983) Z Tierzuecht Zuechtungsbiol. , vol.100 , pp. 27-32
    • Meyer, K.1    Hill, W.G.2
  • 42
    • 58149330808 scopus 로고    scopus 로고
    • Perils of parsimony: Properties of reduced rank estimates of genetic covariances
    • MEYER, K., and M. KIRKPATRICK, 2008 Perils of parsimony: properties of reduced rank estimates of genetic covariances. Genetics 108: 1153-1166.
    • (2008) Genetics , vol.108 , pp. 1153-1166
    • Meyer, K.1    Kirkpatrick, M.2
  • 43
    • 0000202955 scopus 로고
    • A numerical procedure to generate a sample covariance matrix
    • ODELL, P. L., and A. H. FEIVESON, 1966 A numerical procedure to generate a sample covariance matrix. J. Am. Stat. Assoc. 61: 199-203.
    • (1966) J. Am. Stat. Assoc. , vol.61 , pp. 199-203
    • Odell, P.L.1    Feiveson, A.H.2
  • 44
    • 33847302479 scopus 로고    scopus 로고
    • Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach
    • OPGEN-RHEIN, R., and K. STRIMMER, 2007 Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Stat. Appl. Genet. Mol. Biol. 6: 9.
    • (2007) Stat. Appl. Genet. Mol. Biol. , vol.6 , pp. 9
    • Opgen-Rhein, R.1    Strimmer, K.2
  • 45
    • 21444460810 scopus 로고    scopus 로고
    • Unconstrained parameterizations for variance-covariance matrices
    • PINHEIRO, J. C., and D. M. BATES, 1996 Unconstrained parameterizations for variance-covariance matrices. Stat. Comput. 6: 289-296.
    • (1996) Stat. Comput. , vol.6 , pp. 289-296
    • Pinheiro, J.C.1    Bates, D.M.2
  • 46
    • 0012806293 scopus 로고    scopus 로고
    • Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation
    • POURAHMADI, M., 1999 Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation. Biometrika 86: 677-690.
    • (1999) Biometrika , vol.86 , pp. 677-690
    • Pourahmadi, M.1
  • 47
    • 0034221263 scopus 로고    scopus 로고
    • Genetic analyses of live-animal ultrasound and abattoir carcass traits in Australian Angus and Hereford cattle
    • REVERTER, A., D. J. JOHNSTON, H.-U. GRASER, M. L. WOLCOTT and W. H. UPTON, 2000 Genetic analyses of live-animal ultrasound and abattoir carcass traits in Australian Angus and Hereford cattle. J. Anim. Sci. 78: 1786-1795.
    • (2000) J. Anim. Sci. , vol.78 , pp. 1786-1795
    • Reverter, A.1    Johnston, D.J.2    Graser, H.-U.3    Wolcott, M.L.4    Upton, W.H.5
  • 49
    • 70350337963 scopus 로고    scopus 로고
    • Generalized thresholding of large covariance matrices
    • ROTHMAN, A. J., E. LEVINA and J. ZHU, 2009 Generalized thresholding of large covariance matrices. J. Am. Stat. Assoc. 104: 177-186.
    • (2009) J. Am. Stat. Assoc. , vol.104 , pp. 177-186
    • Rothman, A.J.1    Levina, E.2    Zhu, J.3
  • 51
    • 40749130333 scopus 로고    scopus 로고
    • Sample covariance shrinkage for high dimensional dependent data
    • SANCETTA, A., 2008 Sample covariance shrinkage for high dimensional dependent data. J. Multivar. Anal. 99: 949-967.
    • (2008) J. Multivar. Anal. , vol.99 , pp. 949-967
    • Sancetta, A.1
  • 52
    • 27844521293 scopus 로고    scopus 로고
    • A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics
    • SCHÄFER, J., and K. STRIMMER, 2005 A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat. Appl. Genet. Mol. Biol. 4: 32.
    • (2005) Stat. Appl. Genet. Mol. Biol. , vol.4 , pp. 32
    • Schäfer, J.1    Strimmer, K.2
  • 53
    • 0033234634 scopus 로고    scopus 로고
    • Improved non-negative estimation of multivariate components of variance
    • SRIVASTAVA, M. S., and T. KUBOKAWA, 1999 Improved non-negative estimation of multivariate components of variance. Ann. Stat. 27: 2008-2032.
    • (1999) Ann. Stat. , vol.27 , pp. 2008-2032
    • Srivastava, M.S.1    Kubokawa, T.2
  • 55
    • 0017051553 scopus 로고
    • The estimation of maternal genetic variance
    • THOMPSON, R., 1976 The estimation of maternal genetic variance. Biometrics 32: 903-917.
    • (1976) Biometrics , vol.32 , pp. 903-917
    • Thompson, R.1
  • 57
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • TIBSHIRANI, R., 1996 Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58: 267-288.
    • (1996) J. R. Stat. Soc. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 58
    • 67650653486 scopus 로고    scopus 로고
    • Penalized regression with correlation-based penalty
    • TUTZ, G., and J. ULBRICHT, 2009 Penalized regression with correlation-based penalty. Stat. Comput. 19: 239-253.
    • (2009) Stat. Comput. , vol.19 , pp. 239-253
    • Tutz, G.1    Ulbricht, J.2
  • 59
    • 42349090022 scopus 로고    scopus 로고
    • Penalized normal likelihood and ridge regularization of correlation and covariance matrices
    • WARTON, D. I., 2008 Penalized normal likelihood and ridge regularization of correlation and covariance matrices. J. Am. Stat. Assoc. 103: 340-349.
    • (2008) J. Am. Stat. Assoc. , vol.103 , pp. 340-349
    • Warton, D.I.1
  • 60
    • 70450278707 scopus 로고    scopus 로고
    • Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci
    • YAP, J. S., J. FAN and R. WU, 2009 Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci. Biometrics 65: 1068-1077.
    • (2009) Biometrics , vol.65 , pp. 1068-1077
    • Yap, J.S.1    Fan, J.2    Wu, R.3
  • 61
    • 60449112149 scopus 로고    scopus 로고
    • Improved estimation of the covariance matrix under Stein's loss
    • YE, R. D., and S. G. WANG, 2009 Improved estimation of the covariance matrix under Stein's loss. Stat. Probab. Lett. 79: 715-721.
    • (2009) Stat. Probab. Lett. , vol.79 , pp. 715-721
    • Ye, R.D.1    Wang, S.G.2
  • 62
    • 16244401458 scopus 로고    scopus 로고
    • Regularization and variable selection via the elastic net
    • ZOU, H., and T. HASTIE, 2005 Regularization and variable selection via the elastic net. J. R. Stat. Soc. B 67: 301-320.
    • (2005) J. R. Stat. Soc. B , vol.67 , pp. 301-320
    • Zou, H.1    Hastie, T.2


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