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Articles

Cholesky-based model averaging for covariance matrix estimation

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Pages 48-58 | Received 01 Mar 2017, Accepted 29 May 2017, Published online: 28 Jul 2017

References

  • Bickel, P., & Levina, E. (2008a). Covariance regularization by thresholding. The Annals of Statistics, 36, 2577–2604.
  • Bickel, P., & Levina, E. (2008b). Regularized estimation of large covariance matrices. The Annals of Statistics, 36, 199–227.
  • Bien, J., & Tibshirani, R. (2011). Sparse estimation of a covariance matrix. Biometrika, 98, 807–820.
  • Burman, P. (1989). A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika, 76, 503–514.
  • Chen, Z., & Leng, C. (2015). Local linear estimation of covariance matrices via Cholesky decomposition. Statistica Sinica, 25, 1249–1263.
  • Cochran, W. G. (1977). Sampling techniques. New York, NY: John Wiley & Sons.
  • Deng, X., & Tsui, K.-W. (2013). Penalized covariance matrix estimation using a Matrix-Logarithm transformation. Journal of Computational and Graphical Statistics, 22, 494–512.
  • Fan, J., Xue, L., & Zou, H. (2016). Multitask quantile regression under the transnormal model. Journal of the American Statistical Association, 111, 1726–1735.
  • Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1–22.
  • Golub, G. H., & Van Loan, C. F. (2012). Matrix computations. Baltimore, MD: The Johns Hopkins University Press.
  • Hunter, D. R., & Lange, K. (2000). Quantile regression via an MM algorithm. Journal of Computational and Graphical Statistics, 9, 60–77.
  • James, W., & Stein, C. (1961). Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 361–379.
  • Johnstone, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. The Annals of Statistics, 29, 295–327.
  • Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22, 79–86.
  • Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88, 365–411.
  • 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.
  • Liu, H., Wang, L., & Zhao, T. (2013). Sparse covariance matrix estimation with eigenvalue constraints. Journal of Computational and Graphical Statistics, 23, 439–459.
  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7, 77–91.
  • Michaud, R. O. (1989). The Markowitz optimization enigma: Is ‘optimized’ optimal? Financial Analysts Journal, 45, 31–42.
  • Pinheiro, J. C., & Bates, D. M. (1996). Unconstrained parametrizations for variance-covariance matrices. Statistics and Computing, 6, 289–296.
  • Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation. Biometrika, 86, 677–690.
  • Rothman, A., Levina, E., & Zhu, J. (2010). A new approach to Cholesky-based covariance regularization in high dimensions. Biometrika, 97, 539–550.
  • Trefethen, L. N., & Bau III, D. (1997). Numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics.
  • Wang, Y., & Daniels, M. (2014). Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor. Journal of multivariate analysis, 130, 21–26.
  • Xue, L., Ma, S., & Zou, H. (2012). Positive definite l1 penalized estimation of large covariance matrices. Journal of the American Statistical Association, 107, 1480–1491.

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