References
- Wright SJ, Nocedal J. Numerical optimization. Berlin: Springer; 1999.
- Markowitz H. Portfolio selection. J Financ. 1952;7(1):77–91.
- Ledoit O, Wolf M. A well-conditioned estimator for large-dimensional covariance matrices. J Multivariate Anal. 2004;88(2):365–411. doi: 10.1016/S0047-259X(03)00096-4
- Ledoit O, Wolf M. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J Empir Financ. 2003;10(5):603–621. doi: 10.1016/S0927-5398(03)00007-0
- Disatnik DJ, Benninga S. Shrinking the covariance matrix. J Portfolio Manag. 2007;33(4):55–63. doi: 10.3905/jpm.2007.690606
- Fan J, Zhang J, Yu K. Vast portfolio selection with gross-exposure constraints. J Am Stat Assoc. 2012;107(498):592–606. doi: 10.1080/01621459.2012.682825
- Xue L, Ma S, Zou H. Positive-definite l1-penalized estimation of large covariance matrices. J Am Stat Assoc. 2012;107(500):1480–1491. doi: 10.1080/01621459.2012.725386
- Won JH, Lim J, Kim SJ, et al. Condition-number-regularized covariance estimation. J R Stat Soc Ser B Stat Methodol. 2013;75(3):427–450. doi: 10.1111/j.1467-9868.2012.01049.x
- Liu H, Wang L, Zhao T. Sparse covariance matrix estimation with eigenvalue constraints. J Comput Graph Stat. 2014;23(2):439–459. doi: 10.1080/10618600.2013.782818
- Guo X, Zhang C. The effect of L1 penalization on condition number constrained estimation of precision matrix. Stat Sinica. 2017;27:1299–1317.
- Brandt MW. Portfolio choice problems. In: Ait-Sahalia Y, Hansen LP, editors, Handbook of financial econometrics: Tools and techniques. Amsterdam: North-Holland Publishing Company; 2009. p. 269–336.
- Best MJ, Grauer RR. Sensitivity analysis for mean-variance portfolio problems. Manag Sci. 1991;37(8):980–989. doi: 10.1287/mnsc.37.8.980
- Guigues V. Sensitivity analysis and calibration of the covariance matrix for stable portfolio selection. Comput Opt Appl. 2011;48(3):553–579. doi: 10.1007/s10589-009-9260-7
- Li J. Sparse and stable portfolio selection with parameter uncertainty. J Bus Econom Stat. 2015;33(3):381–392. doi: 10.1080/07350015.2014.954708
- Rice JR. A theory of condition. SIAM J Numer Anal. 1966;3(2):287–310. doi: 10.1137/0703023
- Bürgisser P, Cucker F. Condition: the geometry of numerical algorithms, vol. 349 of grundlehren der mathematischen wissenschaften. Heidelberg: Springer; 2013.
- Gulliksson M, Jin XQ, Wei YM. Perturbation bounds for constrained and weighted least squares problems. Linear Algebra Appl. 2002;349(1–3):221–232. doi: 10.1016/S0024-3795(02)00262-8
- Wei M. Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems. Linear Algebra Appl. 1992;161:27–43. doi: 10.1016/0024-3795(92)90003-S
- Horn RA, Johnson CR. Topics in matrix analysis. New York (NY): Cambridge University Press; 1991.
- Graham A. Kronecker products and matrix calculus: with applications. New York (NY): John Wiley; 1982.
- Cao Y, Petzold L. A subspace error estimate for linear systems. SIAM J Matrix Anal Appl. 2003;24(3):787–801. doi: 10.1137/S0895479801390649
- Geurts AJ. A contribution to the theory of condition. Numer Math. 1982;39:85–96. doi: 10.1007/BF01399313
- Gohberg I, Koltracht I. Mixed, componentwise, and structured condition numbers. SIAM J Matrix Anal Appl. 1993;14:688–704. doi: 10.1137/0614049
- Xie Z, Li W, Jin X. On condition numbers for the canonical generalized polar decomposition of real matrices. Electron J Linear Algebra. 2013;26:842–857. doi: 10.13001/1081-3810.1691
- Higham NJ. Accuracy and stability of numerical algorithms. 2nd ed. Philadelphia (PA): SIAM; 2002.
- Gratton S. On the condition number of linear least squares problems in a weighted Frobenius norm. BIT. 1996;36(3):523–530. doi: 10.1007/BF01731931
- Li H, Wang S. On the partial condition numbers for the indefinite least squares problem. Appl Numer Math. 2018;123:200–220. doi: 10.1016/j.apnum.2017.09.006
- Cucker F, Diao H, Wei Y. On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Math Comput. 2007;76(258):947–963. doi: 10.1090/S0025-5718-06-01913-2
- Diao HA, Liang L, Qiao S. A condition analysis of the weighted linear least squares problem using dual norms. Linear Multilinear Algebra. 2018;66(6)1085–1103. doi: 10.1080/03081087.2017.1337059
- Georgescu DI, Higham NJ, Peters GW. Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance. R Soc Open Sci. 2018;5(3):172348. doi: 10.1098/rsos.172348
- Higham NJ, Strabic N, Sego V. Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block. SIAM Rev. 2016;58(2):245–263. doi: 10.1137/140996112
- Diao HA, Sun Y. Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem. Linear Algebra Appl. 2018;544:1–29. doi: 10.1016/j.laa.2018.01.008
- Wang S, Li H, Yang H. A note on the condition number of the scaled total least squares problem. Calcolo. 2018;55(4): 13. Article 46. doi: 10.1007/s10092-018-0289-9
- Hochstenbach ME. Probabilistic upper bounds for the matrix two-norm. J Sci Comput. 2013;57(3):464–476. doi: 10.1007/s10915-013-9716-x
- Kenney C, Laub A. Small-sample statistical condition estimates for general matrix functions. SIAM J Sci Comput. 1994;15:36–61. doi: 10.1137/0915003
- Li H, Wang S. Partial condition number for the equality constrained linear least squares problem. Calcolo. 2017;54(4):1121–1146. doi: 10.1007/s10092-017-0221-8
- Diao HA, Wei Y, Xie P. Small sample statistical condition estimation for the total least squares problem. Numer Algorithms. 2017;75:435–455. doi: 10.1007/s11075-016-0185-9