메뉴 건너뛰기




Volumn 26, Issue 3, 2017, Pages 682-694

Precision Matrix Estimation With ROPE

Author keywords

Frobenius norm; Penalized likelihood; Riccati equation; Ridge estimate; Shrinkage

Indexed keywords


EID: 85019698520     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2016.1278002     Document Type: Article
Times cited : (26)

References (39)
  • 1
    • 82255195996 scopus 로고    scopus 로고
    • Sparse Estimation of a Covariance Matrix,
    • Bien, J., and Tibshirani, R. J., (2011), “Sparse Estimation of a Covariance Matrix,” Biometrika, 98, 807–820.
    • (2011) Biometrika , vol.98 , pp. 807-820
    • Bien, J.1    Tibshirani, R.J.2
  • 6
    • 84890138173 scopus 로고    scopus 로고
    • Penalized Covariance Matrix Estimation Using a Matrix-Logarithm Transformation,
    • Deng, X., and Tsui, K.-W., (2013), “Penalized Covariance Matrix Estimation Using a Matrix-Logarithm Transformation,” Journal of Computational and Graphical Statistics, 22, 494–512.
    • (2013) Journal of Computational and Graphical Statistics , vol.22 , pp. 494-512
    • Deng, X.1    Tsui, K.-W.2
  • 7
    • 42549144258 scopus 로고    scopus 로고
    • Providence, RI: American Mathematical Society
    • Dym, H., (2007), Linear Algebra in Action, Providence, RI:American Mathematical Society.
    • (2007) Linear Algebra in Action
    • Dym, H.1
  • 8
    • 85136354327 scopus 로고    scopus 로고
    • Ridge Regression and Other Kernels for Genomic Selection With R Package rrBLUP,
    • Endelman, J. B., (2011), “Ridge Regression and Other Kernels for Genomic Selection With R Package rrBLUP,” The Plant Genome, 4, 250–255.
    • (2011) The Plant Genome , vol.4 , pp. 250-255
    • Endelman, J.B.1
  • 9
    • 73949117731 scopus 로고    scopus 로고
    • Network Exploration via the Adaptive LASSO and SCAD Penalties,
    • Fan, J., Feng, Y., and Wu, Y., (2009), “Network Exploration via the Adaptive LASSO and SCAD Penalties,” The Annals of Applied Statistics, 3, 521–541.
    • (2009) The Annals of Applied Statistics , vol.3 , pp. 521-541
    • Fan, J.1    Feng, Y.2    Wu, Y.3
  • 10
    • 45849134070 scopus 로고    scopus 로고
    • Sparse Inverse Covariance Estimation With the Graphical Lasso,
    • Friedman, J., Hastie, T., and Tibshirani, R., (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
  • 11
    • 0016704147 scopus 로고
    • Best Linear Unbiased Estimation and Prediction Under a Selection Model,
    • Henderson, C. R., (1975), “Best Linear Unbiased Estimation and Prediction Under a Selection Model,” Biometrics, 31, 423–447.
    • (1975) Biometrics , vol.31 , pp. 423-447
    • Henderson, C.R.1
  • 12
    • 0034288884 scopus 로고    scopus 로고
    • Numerical Analysis of a Quadratic Matrix Equation,
    • Highman, N. J., and Kim, H.-M., (2000), “Numerical Analysis of a Quadratic Matrix Equation,” IMA Journal of Numerical Analysis, 20, 499–519.
    • (2000) IMA Journal of Numerical Analysis , vol.20 , pp. 499-519
    • Highman, N.J.1    Kim, H.-M.2
  • 13
    • 33644986127 scopus 로고    scopus 로고
    • Covariance Selection and Estimation via Penalised Normal Likelihood,
    • Huang, J. Z., Liu, N., Pourahmadi, M., and Liu, L., (2006), “Covariance 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
  • 14
    • 84958818558 scopus 로고    scopus 로고
    • Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation,
    • Kuismin, M., and Sillanpää, M. J., (2016), “Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation,” PLOS ONE, 11, e0148171.
    • (2016) PLOS ONE , vol.11 , pp. e0148171
    • Kuismin, M.1    Sillanpää, M.J.2
  • 15
    • 84906309235 scopus 로고    scopus 로고
    • Algorithms for Solving a Unilateral Quadratic Matrix Equation and the Model Updating Problem,
    • Larin, V. B., (2014), “Algorithms for Solving a Unilateral Quadratic Matrix Equation and the Model Updating Problem,” International Applied Mechanics, 50, 321–334.
    • (2014) International Applied Mechanics , vol.50 , pp. 321-334
    • Larin, V.B.1
  • 16
    • 0018681625 scopus 로고
    • A Schur Method for Solving Algebraic Riccati Equations,
    • Laub, A. J., (1979), “A Schur Method for Solving Algebraic Riccati Equations,” IEEE Transactions on Automatic Control, 24, 913–921.
    • (1979) IEEE Transactions on Automatic Control , vol.24 , pp. 913-921
    • Laub, A.J.1
  • 17
    • 4344637588 scopus 로고    scopus 로고
    • Honey, I Shrunk the Sample Covariance Matrix,
    • Ledoit, O., and Wolf, M., (2004a), “Honey, I Shrunk the Sample Covariance Matrix,” The Journal of Portfolio Management, 30, 110–119.
    • (2004) The Journal of Portfolio Management , vol.30 , pp. 110-119
    • Ledoit, O.1    Wolf, M.2
  • 18
    • 0346961488 scopus 로고    scopus 로고
    • A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices,
    • ——— (2004b), “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices,” Journal of Multivariate Analysis, 88, 365–411.
    • (2004) Journal of Multivariate Analysis , vol.88 , pp. 365-411
  • 19
    • 84872012313 scopus 로고    scopus 로고
    • Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices,
    • ——— (2012), “Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices,” The Annals of Statistics, 40, 1024–1060.
    • (2012) The Annals of Statistics , vol.40 , pp. 1024-1060
  • 20
    • 84947924016 scopus 로고    scopus 로고
    • Spectrum Estimation: A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions,
    • ——— (2015), “Spectrum Estimation:A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions,” Journal of Multivariate Analysis, 139, 360–384.
    • (2015) Journal of Multivariate Analysis , vol.139 , pp. 360-384
  • 21
    • 84866898119 scopus 로고    scopus 로고
    • Overview of LASSO-Related Penalized Regression Methods for Quantitative Trait Mapping and Genomic Selection,
    • Li, Z., and Sillanpää, M. J., (2012), “Overview of LASSO-Related Penalized Regression Methods for Quantitative Trait Mapping and Genomic Selection,” Theoretical and Applied Genetics, 125, 419–435.
    • (2012) Theoretical and Applied Genetics , vol.125 , pp. 419-435
    • Li, Z.1    Sillanpää, M.J.2
  • 22
    • 84921526590 scopus 로고    scopus 로고
    • Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions,
    • Liu, W., and Luo, X., (2015), “Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions,” Journal of Multivariate Analysis, 135, 153–162.
    • (2015) Journal of Multivariate Analysis , vol.135 , pp. 153-162
    • Liu, W.1    Luo, X.2
  • 24
    • 33747163541 scopus 로고    scopus 로고
    • High Dimensional Graphs and Variable Selection With the LASSO,
    • Meinshausen, N., and Bühlmann, P., (2006), “High Dimensional Graphs and Variable Selection With the LASSO,” The Annals of Statistics, 34, 1436–1462.
    • (2006) The Annals of Statistics , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 25
    • 84925492068 scopus 로고    scopus 로고
    • Shrinkage Estimation of the Genomic Relationship Matrix Can Improve Genomic Estimated Breeding Values in the Training Set,
    • Müller, D., Technow, F., and Melchinger, A. E., (2015), “Shrinkage Estimation of the Genomic Relationship Matrix Can Improve Genomic Estimated Breeding Values in the Training Set,” Theoretical and Applied Genetics, 128, 693–703.
    • (2015) Theoretical and Applied Genetics , vol.128 , pp. 693-703
    • Müller, D.1    Technow, F.2    Melchinger, A.E.3
  • 26
    • 84897096123 scopus 로고    scopus 로고
    • The FASTCLIME Package for Linear Programming and Large-Scale Precision Matrix Estimation in R,
    • Pang, H., Liu, H., and Vanderbei, R., (2014), “The FASTCLIME Package for Linear Programming and Large-Scale Precision Matrix Estimation in R,” Journal of Machine Learning Research, 15, 489–493.
    • (2014) Journal of Machine Learning Research , vol.15 , pp. 489-493
    • Pang, H.1    Liu, H.2    Vanderbei, R.3
  • 27
    • 77956889208 scopus 로고
    • Recovery of Inter-Block Information When Block Sizes are Unequal,
    • Patterson, H. D., and Thompson, R., (1971), “Recovery of Inter-Block Information When Block Sizes are Unequal,” Biometrika, 58, 545–554.
    • (1971) Biometrika , vol.58 , pp. 545-554
    • Patterson, H.D.1    Thompson, R.2
  • 28
    • 33846006923 scopus 로고    scopus 로고
    • Population Structure and Eigenanalysis,
    • Patterson, N., Price, A. L., and Reich, D., (2006), “Population Structure and Eigenanalysis,” PLOS Genetics, 2, 1–20.
    • (2006) PLOS Genetics , vol.2 , pp. 1-20
    • Patterson, N.1    Price, A.L.2    Reich, D.3
  • 29
    • 85168500140 scopus 로고    scopus 로고
    • Genomic-Enabled Prediction Based on Molecular Markers and Pedigree Using the BLR Package in R
    • Pérez, P., DeLos, C. G., Crossa, J., and Gianola, D., (2010), “Genomic-Enabled Prediction Based on Molecular Markers and Pedigree Using the BLR Package in R,” Plant Genome, 3, 106–116.
    • (2010) Plant Genome , vol.3 , pp. 106-116
    • Pérez, P.1    DeLos, C.G.2    Crossa, J.3    Gianola, D.4
  • 31
    • 0000695717 scopus 로고
    • A Generalization of the Gamma Distribution,
    • Stacy, E. W., (1962), “A Generalization of the Gamma Distribution,” The Annals of Mathematical Statistics, 33, 1187–1192.
    • (1962) The Annals of Mathematical Statistics , vol.33 , pp. 1187-1192
    • Stacy, E.W.1
  • 32
    • 85194972808 scopus 로고    scopus 로고
    • Regression Shrinkage and Selection via the LASSO,
    • Series B
    • Tibshirani, R., (1996), “Regression Shrinkage and Selection via the LASSO,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
    • (1996) Journal of the Royal Statistical Society , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 33
    • 55849133422 scopus 로고    scopus 로고
    • Efficient Methods to Compute Genomic Predictions,
    • VanRaden, P. M., (2008), “Efficient Methods to Compute Genomic Predictions,” Journal of Dairy Science, 91, 4414–4423.
    • (2008) Journal of Dairy Science , vol.91 , pp. 4414-4423
    • VanRaden, P.M.1
  • 34
    • 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,” Journal of the American Statistical Association, 103, 340–349.
    • (2008) Journal of the American Statistical Association , vol.103 , pp. 340-349
    • Warton, D.I.1
  • 35
    • 84974815616 scopus 로고    scopus 로고
    • Ridge Estimation of Inverse Covariance Matrices From High-Dimensional Data,
    • Wieringen, W. N., and Peeters, C. F. W., (2016), “Ridge Estimation of Inverse Covariance Matrices From High-Dimensional Data,” Computational Statistics and Data Analysis, 103, 284–303.
    • (2016) Computational Statistics and Data Analysis , vol.103 , pp. 284-303
    • Wieringen, W.N.1    Peeters, C.F.W.2
  • 38
    • 0001042840 scopus 로고
    • On a Matrix Riccati Equation of Stochastic Control,
    • Wonham, W. M., (1968), “On a Matrix Riccati Equation of Stochastic Control,” SIAM Journal on Control, 6, 681–697.
    • (1968) SIAM Journal on Control , vol.6 , pp. 681-697
    • Wonham, W.M.1
  • 39
    • 84884790280 scopus 로고    scopus 로고
    • A Coordinate Descent Algorithm for Sparse Positive Definite Matrix Estimation,
    • Yuan, T., and Wang, J., (2013), “A Coordinate Descent Algorithm for Sparse Positive Definite Matrix Estimation,” Statistical Analysis and Data Mining, 6, 431–442.
    • (2013) Statistical Analysis and Data Mining , vol.6 , pp. 431-442
    • Yuan, T.1    Wang, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.