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Theory and Methods

Are Latent Factor Regression and Sparse Regression Adequate?

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Pages 1076-1088 | Received 13 Jan 2022, Accepted 13 Jan 2023, Published online: 14 Feb 2023

References

  • Ahn, S. C., and Horenstein, A. R. (2013), “Eigenvalue Ratio Test for the Number of Factors,” Econometrica, 81, 1203–1227.
  • Avella-Medina, M., Battey, H. S., Fan, J., and Li, Q. (2018), “Robust Estimation of High-Dimensional Covariance and Precision Matrices,” Biometrika, 105, 271–284. DOI: 10.1093/biomet/asy011.
  • Bai, J. (2003), “Inferential Theory for Factor Models of Large Dimensions,” Econometrica, 71, 135–171. DOI: 10.1111/1468-0262.00392.
  • Bai, J., and Li, K. (2012), “Statistical Analysis of Factor Models of High Dimension.,” The Annals of Statistics, 40, 436–465. DOI: 10.1214/11-AOS966.
  • 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. (2006), “Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions,” Econometrica, 74, 1133–1150.
  • Bai, J. (2008), “Forecasting Economic Time Series Using Targeted Predictors,” Journal of Econometrics, 146, 304–317. DOI: 10.1016/j.jeconom.2008.08.010.
  • Bair, E., Hastie, T., Paul, D., and Tibshirani, R. (2006), “Prediction by Supervised Principal Components,” Journal of the American Statistical Association, 101, 119–137. DOI: 10.1198/016214505000000628.
  • Barut, E., Fan, J., and Verhasselt, A. (2016), “Conditional Sure Independence Screening,” Journal of the American Statistical Association, 111, 1266–1277. DOI: 10.1080/01621459.2015.1092974.
  • Belloni, A., and Chernozhukov, V. (2011), “l1-Penalized Quantile Regression in High-Dimensional Sparse Models,” The Annals of Statistics, 39, 82–130.
  • Bianchi, D., Büchner, M., and Tamoni, A. (2021), “Bond Risk Premiums with Machine Learning,” The Review of Financial Studies, 34, 1046–1089. DOI: 10.1093/rfs/hhaa062.
  • Bing, X., Bunea, F., and Wegkamp, M. (2019), “Inference in Latent Factor Regression with Clusterable Features,” arXiv:1905.12696.
  • Bing, X., Bunea, F., Strimas-Mackey, S., and Wegkamp, M. (2021), “Prediction under Latent Factor Regression: Adaptive pcr, Interpolating Predictors and Beyond,” Journal of Machine Learning Research, 22, 1–50.
  • Bunea, F., Strimas-Mackey, S., and Wegkamp, M. (2020), “Interpolating Predictors in High-Dimensional Factor Regression,” arXiv:2002.02525.
  • Cai, 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.
  • Candes, E., and Tao, T. (2007), “The Dantzig Selector: Statistical Estimation When p is much Larger than n,” The Annals of Statistics, 35, 2313–2351. DOI: 10.1214/009053606000001523.
  • Chernozhukov, V., Chetverikov, D., and Kato, K. (2013), “Gaussian Approximations and Multiplier Bootstrap for Maxima of Sums of High-Dimensional Random Vectors,” The Annals of Statistics, 41, 2786–2819. DOI: 10.1214/13-AOS1161.
  • Chernozhukov, V. (2017), “Central Limit Theorems and Bootstrap in High Dimensions,” Annals of Probability, 45, 2309–2352.
  • Chernozhukov, V., Chetverikov, D., and Koike, Y. (2020), “Nearly Optimal Central Limit Theorem and Bootstrap Approximations in High Dimensions,” arXiv preprint arXiv:2012.09513.
  • Chu, W., Li, R., and Reimherr, M. (2016), “Feature Screening for Time-Varying Coefficient Models with Ultrahigh Dimensional Longitudinal Data,” The Annals of Applied Statistics, 10, 596–617. DOI: 10.1214/16-AOAS912.
  • Coulombe, P. G., Leroux, M., Stevanovic, D., and Surprenant, S. (2021), “Macroeconomic Data Transformations Matter,” International Journal of Forecasting, 37, 1338–1354. DOI: 10.1016/j.ijforecast.2021.05.005.
  • Coulombe, P. G., Marcellino, M., and Stevanović, D. (2021), “Can Machine Learning Catch the Covid-19 Recession?” National Institute Economic Review, 256, 71–109. DOI: 10.1017/nie.2021.10.
  • Dezeure, R., Bühlmann, P., and Zhang, C.-H. (2017), “High-Dimensional Simultaneous Inference with the Bootstrap,” Test, 26, 685–719. DOI: 10.1007/s11749-017-0554-2.
  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” The Annals of Statistics, 32, 407–499. DOI: 10.1214/009053604000000067.
  • 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. DOI: 10.1198/016214501753382273.
  • Fan, J., and Liao, Y. (2020), “Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors,” Journal of the American Statistical Association, 117, 909–924. DOI: 10.1080/01621459.2020.1831927.
  • Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911. DOI: 10.1111/j.1467-9868.2008.00674.x.
  • Fan, J. (2011), “Nonconcave Penalized Likelihood with NP-Dimensionality,” IEEE Transactions on Information Theory, 57, 5467–5484.
  • Fan, J., and Song, R. (2010), “Sure Independence Screening in Generalized Linear Models with NP-Dimensionality,” The Annals of Statistics, 38, 3567–3604. DOI: 10.1214/10-AOS798.
  • Fan, J., Guo, S., and Hao, N. (2012), “Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression,” Journal of the Royal Statistical Society, Series B, 74, 37–65. DOI: 10.1111/j.1467-9868.2011.01005.x.
  • Fan, J., Liao, Y., and Mincheva, M. (2013), “Large Covariance Estimation by Thresholding Principal Orthogonal Complements,” Journal of the Royal Statistical Society, Series B, 75, 603–680. With 33 discussions by 57 authors and a reply by Fan, Liao and Mincheva. DOI: 10.1111/rssb.12016.
  • Fan, J., Fan, Y., and Barut, E. (2014), “Adaptive Robust Variable Selection,” The Annals of Statistics, 42, 324–351. DOI: 10.1214/13-AOS1191.
  • Fan, J., Li, Q., and Wang, Y. (2017), “Estimation of High Dimensional Mean Regression in the Absence of Symmetry and Light Tail Assumptions,” Journal of the Royal Statistical Society, Series B, 79, 247–265. DOI: 10.1111/rssb.12166.
  • Fan, J., Xue, L., and Yao, J. (2017), “Sufficient Forecasting Using Factor Models,” Journal of Econometrics, 201, 292–306. DOI: 10.1016/j.jeconom.2017.08.009.
  • 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.
  • Fan, J., Li, R., Zhang, C.-H., and Zou, H. (2020), “Statistical Foundations of Data Science, Boca Raton, FL: CRC Press.
  • Fan, J., Masini, R., and Medeiros, M. C. (2021), “Bridging Factor and Sparse Models,” arXiv:2102.11341.
  • Fan, J., Yang, Z., and Yu, M. (2021), “Understanding Implicit Regularization in Over-Parameterized Single Index Model,” arXiv:2007.08322v3. DOI: 10.1080/01621459.2022.2044824.
  • Fan, J., Guo, J., and Zheng, S. (2022), “Estimating Number of Factors by Adjusted Eigenvalues Thresholding,” Journal of the American Statistical Association, 117, 852–861. DOI: 10.1080/01621459.2020.1825448.
  • 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.
  • Goulet Coulombe, P. (2020), “The Macroeconomy as a Random Forest,” Available at SSRN 3633110.
  • Hall, A. S. (2018), “Machine Learning Approaches to Macroeconomic Forecasting,” The Federal Reserve Bank of Kansas City Economic Review, 103, 63–81.
  • Hernan, M., and Robins, J. (2019), Causal Inference. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Boca Raton, FL: CRC Press.
  • Hotelling, H. (1933), “Analysis of a Complex of Statistical Variables into Principal Components,” Journal of Educational Psychology, 24, 417–441. DOI: 10.1037/h0071325.
  • Imbens, G., and Rubin, D. (2015), Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction, New York: Cambridge University Press.
  • Javanmard, A., and Montanari, A. (2014), “Confidence Intervals and Hypothesis Testing for High-Dimensional Regression,” Journal of Machine Learning Research, 15, 2869–2909.
  • 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.
  • 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.
  • Lam, C., and Yao, Q. (2012), “Factor Modeling for High-Dimensional Time Series: Inference for the Number of Factors,” The Annals of Statistics, 40, 694–726. DOI: 10.1214/12-AOS970.
  • Li, G., Peng, H., Zhang, J., and Zhu, L. (2012), “Robust Rank Correlation based Screening,” The Annals of Statistics, 40, 1846–1877. DOI: 10.1214/12-AOS1024.
  • Li, Q., and Li, L. (2021), “Integrative Factor Regression and its Inference for Multimodal Data Analysis,” Journal of the American Statistical Association, 113, 1–15.
  • Li, Q., Cheng, G., Fan, J., and Wang, Y. (2018), “Embracing the Blessing of Dimensionality in Factor Models,” Journal of the American Statistical Association, 113, 380–389. DOI: 10.1080/01621459.2016.1256815.
  • Lin, J., and Michailidis, G. (2020), “System Identification of High-Dimensional Linear Dynamical Systems with Serially Correlated Output Noise Components,” IEEE Transactions on Signal Processing, 68, 5573–5587. DOI: 10.1109/TSP.2020.3020397.
  • Liu, J., Li, R., and Wu, R. (2014), “Feature Selection for Varying Coefficient Models with Ultrahigh-Dimensional Covariates,” Journal of the American Statistical Association, 109, 266–274. DOI: 10.1080/01621459.2013.850086.
  • Loh, P.-L., and Wainwright, M. J. (2012), “High-Dimensional Regression with Noisy and Missing Data: Provable Guarantees with Nonconvexity,” The Annals of Statistics, 40, 1637–1664. DOI: 10.1214/12-AOS1018.
  • Luciani, M. (2014), “Forecasting with Approximate Dynamic Factor Models: The Role of Non-Pervasive Shocks,” International Journal of Forecasting, 30, 20–29. DOI: 10.1016/j.ijforecast.2013.05.001.
  • 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.
  • Nickl, R., and Van De Geer, S. (2013), “Confidence Sets in Sparse Regression,” The Annals of Statistics, 41, 2852–2876. DOI: 10.1214/13-AOS1170.
  • Peng, B., Wang, L., and Wu, Y. (2016), “An Error Bound for L1-norm Support Vector Machine Coefficients in Ultra-High Dimension,” Journal of Machine Learning Research, 17, 8279–8304.
  • Saldana, D. F., and Feng, Y. (2018), “Sis: An r Package for Sure Independence Screening in Ultrahigh-Dimensional Statistical Models,” Journal of Statistical Software, 83, 1–25. DOI: 10.18637/jss.v083.i02.
  • Shi, C., Song, R., Chen, Z., and Li, R. (2019), “Linear Hypothesis Testing for High Dimensional Generalized Linear Models,” The Annals of Statistics, 47, 2671–2703. DOI: 10.1214/18-AOS1761.
  • Smeekes, S., and Wijler, E. (2018), “Macroeconomic Forecasting Using Penalized Regression Methods,” International Journal of Forecasting, 34, 408–430. DOI: 10.1016/j.ijforecast.2018.01.001.
  • 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.
  • Sun, Q., Zhou, W.-X., and Fan, J. (2020), “Adaptive Huber Regression,” Journal of the American Statistical Association, 115, 254–265. DOI: 10.1080/01621459.2018.1543124.
  • Sun, T., and Zhang, C.-H. (2012), “Scaled Sparse Linear Regression,” Biometrika, 99, 879–898. DOI: 10.1093/biomet/ass043.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series A, 58, 267–288. DOI: 10.1111/j.2517-6161.1996.tb02080.x.
  • Van de Geer, S. (2008), “High-Dimensional Generalized Linear Models and the Lasso,” The Annals of Statistics, 36, 614–645. DOI: 10.1214/009053607000000929.
  • van de Geer, S., Bühlmann, P., Ritov, Y., and Dezeure, R. (2014), “On Asymptotically Optimal Confidence Regions and Tests for High-Dimensional Models,” The Annals of Statistics, 42, 1166–1202. DOI: 10.1214/14-AOS1221.
  • Wang, W., and Fan, J. (2017), “Asymptotics of Empirical Eigenstructure for High Dimensional Spiked Covariance,” The Annals of Statistics, 45, 1342–1374. DOI: 10.1214/16-AOS1487.
  • Wang, X., and Leng, C. (2016), “High Dimensional Ordinary Least Squares Projection for Screening Variables,” Journal of the Royal Statistical Society, Series B, 78, 589–611. DOI: 10.1111/rssb.12127.
  • Yu, G., and Bien, J. (2019), “Estimating the Error Variance in a High-Dimensional Linear Model,” Biometrika, 106, 533–546. DOI: 10.1093/biomet/asz017.
  • Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
  • Zhang, C.-H., and Zhang, S. S. (2014), “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models,” Journal of the Royal Statistical Society, Series B, 76, 217–242. DOI: 10.1111/rssb.12026.
  • Zhang, N., Jiang, W., and Lan, Y. (2019), “On the Sure Screening Properties of Iteratively Sure Independence Screening Algorithms,” arXiv:1812.01367.
  • Zhang, X., and Cheng, G. (2017), “Simultaneous Inference for High-Dimensional Linear Models,” Journal of the American Statistical Association, 112, 757–768. DOI: 10.1080/01621459.2016.1166114.
  • Zhang, X., Wu, Y., Wang, L., and Li, R. (2016), “Variable Selection for Support Vector Machines in Moderately High Dimensions,” Journal of the Royal Statistical Society, Series B, 78, 53–76. DOI: 10.1111/rssb.12100.
  • Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” Journal of Machine Learning Research, 7, 2541–2563.
  • Zhao, P., Yang, Y., and He, Q.-C. (2019), “Implicit Regularization via Hadamard Product Over-Parametrization in High-Dimensional Linear Regression,” arXiv:1903.09367.
  • Zhu, L.-P., Li, L., Li, R., and Zhu, L.-X. (2011), “Model-Free Feature Screening for Ultrahigh-Dimensional Data,” Journal of the American Statistical Association, 106, 1464–1475. DOI: 10.1198/jasa.2011.tm10563.
  • Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429. DOI: 10.1198/016214506000000735.

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