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Theory and Methods

Covariance Regression Analysis

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Pages 266-281 | Received 01 Feb 2015, Published online: 03 May 2017

References

  • Akerlof, G. A. (1997), “Social Distance and Social Decisions,” Econometrica, 65, 1005–1027.
  • Anderson, T. W. (1973), “Asymptotically Efficient Estimation of Covariance Matrices With Linear Structure,” The Annals of Statistics, 1, 135–141.
  • Bai, Z. (1999), “Methodologies in Spectral Analysis of Large-Dimensional Random Matrices, a Review,” Statistica Sinica, 9, 611–677.
  • Bickel, P. J., and Levina, E. (2008a), “Covariance Regularization by Thresholding,” The Annals of Statistics, 36, 2577–2604.
  • ——— (2008b), “Regularized Estimation of Large Covariance Matrices,” The Annals of Statistics, 36, 199–227.
  • Bilmes, J. A. (2000), “Factored Sparse Inverse Covariance Matrices,” 2000 IEEE International Conference, 2, 1009–1012.
  • Bivand, R. S., Pebesma, E. J., and Gómez-Rubio, V. (2008), Applied Spatial Data Analysis With R, New York: Springer.
  • Bodie, Z., Kane, A., and Marcus, A. J. (2009), Investments, New York: McGraw-Hill.
  • Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2011), “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends in Machine Learning, 3, 1–122.
  • Brock, W. A., and Durlauf, S. N. (2001), “Discrete Choice With Social Interactions,” The Review of Economic Studies, 68, 235–260.
  • Cai, T. T., and Jiang, T. (2011), “Limiting Laws of Coherence of Random Matrices With Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices,” The Annals of Statistics, 39, 1496–1525.
  • Cai, T. T., and Liu, W. (2011), “Adaptive Thresholding for Sparse Covariance Matrix Estimation,” Journal of the American Statistical Association, 106, 672–684.
  • Cai, T. T., Liu, W., and Luo, X. (2011), “A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation,” Journal of the American Statistical Association, 106, 594–607.
  • Chan, L. K., Karceski, J., and Lakonishok, J. (1998), “The Risk and Return From Factors,” Journal of Financial and Quantitative Analysis, 33, 159–188.
  • ——— (1999), “On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model,” Review of Financial Studies, 12, 937–974.
  • Chen, X., and Conley, T. G. (2001), “A New Semiparametric Spatial Model for Panel Time Series,” Journal of Econometrics, 105, 59–83.
  • Chiu, T. Y. M., Leonard, T., and Tsui, K.-W. (1996), “The Matrix-Logarithmic Covariance Model,” Journal of the American Statistical Association, 91, 198–210.
  • Cressie, N. (1991), Statistics for Spatial Data, Wiley Series in Probability and Statistics, New York: Wiley.
  • Cressie, N., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley.
  • DeMiguel, V., Garlappi, L., Nogales, F. J., and Uppal, R. (2009), “A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms,” Management Science, 55, 798–812.
  • Demidenko, E. (2004), Mixed Models – Theory and Applications, Hoboken, NJ: Wiley.
  • Dempster, A. P. (1972), “Covariance Selection,” Biometrics, 28, 157–175.
  • Diggle, P. J., Heagerty, P. J., Liang, K.-Y., and Zeger, S. L. (2002), Analysis of Longitudinal Data ( 2nd ed.), Oxford, UK: Oxford University Press.
  • Fama, E. F. (1970), “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance, 25, 383–417.
  • Fan, J., Fan, Y., and Lv, J. (2008), “High Dimensional Covariance Matrix Estimation Using a Factor Model,” Journal of Econometrics, 147, 186–197.
  • Fan, J., Han, F., and Liu, H. (2014), “PAGE: Robust Pattern Guided Estimation of Large Covariance Matrix,” Technical Report. Princeton, NJ: Princeton University.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
  • Fan, J., Liao, Y., and Mincheva, M. (2011), “High Dimensional Covariance Matrix Estimation in Approximate Factor Models,” The Annals of Statistics, 39, 3320–3356.
  • Fletcher, R. (1987), Practical Methods of Optimization, New York: Wiley.
  • Fortin, M., and Glowinski, R. (1983), Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, Amsterdam: North-Holland.
  • Friedman, J., Hastie, T., and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation With the Graphical Lasso,” Biostatistics, 9, 432–441.
  • Glaeser, E. L., Sacerdote, B., and Scheinkman, J. A. (1996), “Crime and Social Interactions,” Quarterly Journal of Economics, 111, 507–548.
  • Gul, F. A., Kim, J. B., and Qiu, A. A. (2010), “Ownership Concentration, Foreign Shareholding, Audit Quality, and Stock Price Synchronicity: Evidence From China,” Journal of Financial Economics, 95, 425–442.
  • Hoff, P. D., and Niu, X. (2012), “A Covariance Regression Model,” Statistica Sinica, 22, 729–753.
  • Huang, J. Z., Liu, N., Pourahmadi, M., and Liu, L. (2006), “Covariance Matrix Selection and Estimation via Penalized Normal Likelihood,” Biometrika, 93, 85–98.
  • Jagannathan, R., and Ma, T. (2003), “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps,” Journal of Finance, 58, 1651–1684.
  • Johnson, R. A., and Wichern, D. W. (1992), Applied Multivariate Statistical Analysis, Englewood Cliffs, NJ: Prentice Hall.
  • Johnstone, I. M., and Lu, A. Y. (2009), “On Consistency and Sparsity for Principal Components Analysis in High Dimensions,” Journal of the American Statistical Association, 104, 682–693.
  • Kan, R., and Zhou, G. (2007), “Optimal Portfolio Choice With Parameter Uncertainty,” Journal of Financial and Quantitative Analysis, 42, 621–656.
  • Ledoit, O., and Wolf, M. (2004), “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices,” Journal of Multivariate Analysis, 88, 365–411.
  • Leng, C., and Li, B. (2011), “Forward Adaptive Banding for Estimating Large Covariance Matrices,” Biometrika, 98, 821–830.
  • Markowitz, H. (1952), “Portfolio Selection,” The Journal of Finance, 7, 77–91.
  • Prentice, R. L. (1988), “Correlated Binary Regression With Covariates Specific to Each Binary Observation,” Biometrics, 44, 1033–1048.
  • Qiu, Y., and Chen, S. X. (2012), “Test for Bandedness of High-Dimensional Covariance Matrices and Bandwidth Estimation,” The Annals of Statistics, 40, 1285–1314.
  • Roll, R. (1988), “R2,” Journal of Finance, 43, 541–566.
  • Schott, J. R. (1997), Matrix Analysis for Statistics, Hoboken, NJ: Wiley.
  • Scott, J. (1988), “Social Network Analysis,” Sociology, 22, 109–127.
  • Seber, G. A. (2008), A Matrix Handbook for Statisticians. Hoboken, NJ: Wiley.
  • Szatrowski, T. H. (1980), “Necessary and Sufficient Conditions for Explicit Solutions in the Multivariate Normal Estimation Problem for Patterned Means and Covariances,” The Annals of Statistics, 8, 802–810.
  • Tong, T., and Wang, Y. (2007), “Optimal Shrinkage Estimation of Variances With Applications to Microarray Data Analysis,” Journal of the American Statistical Association, 102, 113–122.
  • Wang, H. (2009), “Forward Regression for Ultra-High Dimensional Variable Screening,” Journal of the American Statistical Association, 104, 1512–1524.
  • Wasserman, S. (1994), Social Network Analysis: Methods and Applications, New York: Cambridge University Press.
  • Wooldridge, J. (2012), Introductory Econometrics: A Modern Approach, Mason, OH: Cengage Learning.
  • Xue, L., Ma, S., and Zou, H. (2012), “Positive-Definite ℓ1-Penalized Estimation of Large Covariance Matrices,” Journal of the American Statistical Association, 107, 1480–1491.
  • Yin, J., Geng, Z., Li, R., and Wang, H. (2010), “Nonparametric Covariance Model,” Statistica Sinica, 20, 469–479.
  • Zivot, E., and Wang, J. (2007), Modeling Financial Time Series with S-Plus, New York: Springer.
  • Zwiernik, P., Uhler, C., and Richards, D. (2014), “Maximum Likelihood Estimation for Linear Gaussian Covariance Models,” arXiv preprint, 1408.5604.

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