4,500
Views
2
CrossRef citations to date
0
Altmetric
Theory and Methods

Ridge Regression Under Dense Factor Augmented Models

ORCID Icon
Pages 1566-1578 | Received 23 Sep 2021, Accepted 15 Apr 2023, Published online: 05 Jun 2023

References

  • Abadie, A., Diamond, A., and Hainmueller, J. (2010). “Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program,” Journal of the American Statistical Association, 105, 493–505. DOI: 10.1198/jasa.2009.ap08746.
  • Agarwal, A., Shah, D., Shen, D., and Song, D. (2021) “On Robustness of Principal Component Regression,” Journal of the American Statistical Association, 116, 1731–1745. DOI: 10.1080/01621459.2021.1928513.
  • Alter, O., Brown, P. O., and Botstein, D. (2000). “Singular Value Decomposition for Genome-wide Expression Data Processing and Modeling,” Proceedings of the National Academy of Sciences, 97, 10101–10106. DOI: 10.1073/pnas.97.18.10101.
  • Amjad, M., Shah, D., and Shen, D. (2018). “Robust Synthetic Control,” Journal of Machine Learning Research, 19, 802–852.
  • Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., and Wager, S. (2021). “Synthetic Difference-In-Differences,” American Economic Review, 111, 4088–4118. DOI: 10.1257/aer.20190159.
  • Bai, J. (2003), “Inferential Theory for Factor Models of Large Dimensions,” Econometrica, 71, 135–171. DOI: 10.1111/1468-0262.00392.
  • Bai, J., and Ng, S. (2002), “Determining the Number of Factors in Approximate Factor Models,” Econometrica, 70, 191–221. DOI: 10.1111/1468-0262.00273.
  • Bai, J., and Ng, S. (2021), “Approximate Factor Models with Weaker Loadings,” ArXiv Working Paper arXiv:2109.03773.
  • Bai, Z. D., and Silverstein, J. W. (1998). “No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices,” The Annals of Probability, 26, 316–345. DOI: 10.1214/aop/1022855421.
  • Bai, Z. D., and Silverstein, J. W. (2010), Spectral Analysis of Large Dimensional Random Matrices, New York: Springer.
  • Bergmeir, C., Hyndman, R. J., and Koo, B. (2018), “A Note on the Validity of Cross-Validation for Evaluating Autoregressive Time Series Prediction,” Computational Statistics & Data Analysis, 120, 70–83. DOI: 10.1016/j.csda.2017.11.003.
  • Blum, J., and Eisenberg, B. (1975), “The Law of Large Numbers for Subsequences of a Stationary Process,” The Annals of Probability, 3, 281–288. DOI: 10.1214/aop/1176996398.
  • Blum, J., and Hanson, D.(1960), “On the Mean Ergodic Theorem for Subsequences,” Bulletin of the American Mathematical Society, 66, 308–311. DOI: 10.1090/S0002-9904-1960-10481-8.
  • Bradley, R. C. (1986), “Basic Properties of Strong Mixing Conditions,” in Dependence in Probability and Statistics: A Survey of Recent Results, eds. E. Eberlein and M. S. Taqqu, pp. 165–192, Boston: Birkhäuser.
  • Bradley, R. C. (2005), “Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions,” Probability Surveys, 2, 107–144. DOI: 10.1214/154957805100000104.
  • Cai, T. T., Han, X., and Pan, G. (2020), “Limiting Laws for Divergent Spiked Eigenvalues and Largest Nonspiked Eigenvalue of Sample Covariance Matrices,” The Annals of Statistics, 48, 1255–1280. DOI: 10.1214/18-AOS1798.
  • Carrasco, M., and Rossi, B. (2016), “In-Sample Inference and Forecasting in Misspecified Factor Models,” Journal of Business & Economic Statistics, 34, 313–338. DOI: 10.1080/07350015.2016.1186029.
  • Castle, J. L., Clements, M. P., and Hendry, D. F. (2013), “Forecasting by Factors, by Variables, by Both or Neither?,” Journal of Econometrics, 177, 305–319. DOI: 10.1016/j.jeconom.2013.04.015.
  • Cootes, T. F., Taylor, C. J., Cooper, D. H., and Graham, J. (1995). “Active Shape Models-Their Training and Application,” Computer Vision and Image Understanding, 61, 38–59. DOI: 10.1006/cviu.1995.1004.
  • Davis, R. A., and Mikosch, T. (2009). “Probabilistic Properties of Stochastic Volatility Models,” in Handbook of Financial Time Series, eds. T. G. Andersen, R. A. Davis, J. P. Kreiß, and T. V. Mikosch, pp. 255–267, Berlin: Springer.
  • De Mol, C., Giannone, D., and Reichlin, L. (2008), “Forecasting Using a Large Number of Predictors: Is Bayesian Shrinkage a Valid Alternative to Principal Components?,” Journal of Econometrics, 146, 318–328. DOI: 10.1016/j.jeconom.2008.08.011.
  • Dicker, L. H. (2016). “Ridge Regression and Asymptotic Minimax Estimation Over Spheres of Growing Dimension,” Bernoulli, 22, 1–37. DOI: 10.3150/14-BEJ609.
  • Dobriban, E., and Wager, S. (2018), “High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification,” The Annals of Statistics, 46, 247–279. DOI: 10.1214/17-AOS1549.
  • Fan, J., Ke, Y., and Wang, K. (2020), “Factor-Adjusted Regularized Model Selection,” Journal of Econometrics, 216, 71–85. DOI: 10.1016/j.jeconom.2020.01.006.
  • Giannone, D., Lenza, M., and Primiceri, G. E. (2021), “Economic Predictions with Big Data: The Illusion of Sparsity,” Econometrica, 89, 2409–2437. DOI: 10.3982/ECTA17842.
  • Hastie, T., Tibshirani, R., and Friedman, J. H. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction, New York: Springer.
  • Hastie, T., Montanari, A., Rosset, S., and Tibshirani, R. J. (2022), “Surprises in High-Dimensional Ridgeless Least Squares Interpolation,” The Annals of Statistics, 50, 949–986. DOI: 10.1214/21-aos2133.
  • Hayashi, F. (2000), Econometrics Princeton: Princeton University Press.
  • Hallin, M., and Liska, R. (2007). “The Generalized Dynamic Factor Model: Determining the Number of Factors,” Journal of the American Statistical Association, 102, 603–617. DOI: 10.1198/016214506000001275.
  • Hoerl, A. E., and Kennard, R. W. (1970), “Ridge Regression: Biased Estimation for Nonorthogonal Problems,” Technometrics, 12, 55–67. DOI: 10.1080/00401706.1970.10488634.
  • James, G., Witten, D., Hastie, T., and Tibshirani, R. (2021), An Introduction to Statistical Learning: with Applications in R (2nd ed), New York: Springer.
  • Johnstone, I. M. (2001). “On the Distribution of the Largest Eigenvalue in Principal Components Analysis,” The Annals of Statistics, 29, 295–327. DOI: 10.1214/aos/1009210544.
  • 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. DOI: 10.1198/jasa.2009.0121.
  • Johnstone, I. M., and Paul, D. (2018). “PCA in High Dimensions: An Orientation,” Proceedings of the IEEE, 106, 1277–1292. DOI: 10.1109/JPROC.2018.2846730.
  • Jolliffe, I. T. (1982). “A Note on the Use of Principal Components in Regression,” Journal of the Royal Statistical Society, Series C, 31, 300–303. DOI: 10.2307/2348005.
  • Jung, S., and Marron, J. S. (2009). “PCA Consistency in High Dimension, Low Sample Size Context,” The Annals of Statistics, 37, 4104–4130. DOI: 10.1214/09-AOS709.
  • Kneip, A., and Sarda, P. (2011), “Factor Models and Variable Selection in High-Dimensional Regression Analysis,” The Annals of Statistics, 39, 2410–2447. DOI: 10.1214/11-AOS905.
  • Liu, S., and Dobriban, E. (2020), “Ridge Regression: Structure, Cross-Validation, and Sketching,” in International Conference on Learning Representations.
  • Marčenko, V. A., and Pastur, L. A. (1967). “Distribution of Eigenvalues for Some Sets of Random Matrices,” Mathematics of the USSR-Sbornik, 1, 457–483. DOI: 10.1070/SM1967v001n04ABEH001994.
  • McCracken, M. W., and Ng, S. (2016), “FRED-MD: A Monthly Database for Macroeconomic Research,” Journal of Business & Economic Statistics, 34, 574–589. DOI: 10.1080/07350015.2015.1086655.
  • Mitchell, T. J., and Beauchamp, J. J. (1988), “Bayesian Variable Selection in Linear Regression,” Journal of the American Statistical Association, 83, 1023–1032. DOI: 10.1080/01621459.1988.10478694.
  • Ng, S. (2013), “Variable Selection in Predictive Regressions,” In Handbook of Economic Forecasting (Vol. 2), eds. G. Elliott and A. Timmermann, pp. 752–789, Amsterdam: Elsevier.
  • Onatski, A. (2009). “Testing Hypotheses About the Number of Factors in Large Factor Models,” Econometrica, 77, 1447–1479.
  • Onatski, A. (2012). “Asymptotics of the Principal Components Estimator of Large Factor Models With Weakly Influential Factors,” Journal of Econometrics, 168, 244–258.
  • Onatski, A., and Wang, C. (2021), “Spurious Factor Analysis,” Econometrica, 89, 591–614. DOI: 10.3982/ECTA16703.
  • Paul, D. (2007). “Asymptotics of Sample Eigenstructure for a Large Dimensional Spiked Covariance Model,” Statistica Sinica, 17, 1617–1642.
  • Paul, D., and Silverstein, J. W. (2009). “No Eigenvalues Outside the Support of the Limiting Empirical Spectral Distribution of a Separable Covariance Matrix,” Journal of Multivariate Analysis, 100, 37–57. DOI: 10.1016/j.jmva.2008.03.010.
  • Preisendorfer, R. W. (1988). Principal Component Analysis in Meteorology and Oceanography, Amsterdam: Elsevier.
  • Stock, J. H., and Watson, M. W. (2002), “Forecasting Using Principal Components from a Large Number of Predictors,” Journal of the American Statistical Association, 97, 1167–1179. DOI: 10.1198/016214502388618960.
  • Stock, J. H., and Watson, M. W. (2012), “Generalized Shrinkage Methods for Forecasting Using Many Predictors,” Journal of Business & Economic Statistics, 30, 481–493.
  • Tikhonov, A. N. (1963a), “Regularization of Incorrectly Posed Problems,” Soviet Mathematics Doklady, 4, 1624–1627 (English translation).
  • Tikhonov, A. N. (1963b), “Solution of Incorrectly Formulated Problems and the Regularization Method,” Soviet Mathematics Doklady, 4, 1035–1038 (English translation).