Projected principal component analysis in factor models

Annals of Statistics

Volumn 44, Issue 1, 2016, Pages 219-254

  Fan, Jianqing ^a   Liao, Yuan ^b   Wang, Weichen ^a  

^a PRINCETON UNIVERSITY   (United States)

^b Bldg 142   (United States)

Author keywords

High dimensionality; Loading matrix modeling; Semiparametric factor models; Sieve approximation

Indexed keywords

EID: 85013178156     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/15-AOS1364     Document Type: Article

References (44)

1. AHN, S. C. and HORENSTEIN, A. R. (2013). Eigenvalue ratio test for the number of factors. Econometrica 81 1203-1227. MR3064065
2. AHN, J., MARRON, J. S., MULLER, K. M. and CHI, Y.-Y. (2007). The high-dimension, low-sample-size geometric representation holds under mild conditions. Biometrika 94 760-766. MR2410023
3. ALESSI, L., BARIGOZZI, M. and CAPASSO, M. (2010). Improved penalization for determining the number of factors in approximate factor models. Statist. Probab. Lett. 80 1806-1813. MR2734245
4. ANDREWS, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59 817-858. MR1106513
5. BAI, J. (2003). Inferential theory for factor models of large dimensions. Econometrica 71 135-171. MR1956857
6. BAI, J. and LI, K. (2012). Statistical analysis of factor models of high dimension. Ann. Statist. 40 436-465. MR3014313
7. BAI, J. and NG, S. (2002). Determining the number of factors in approximate factor models. Econometrica 70 191-221. MR1926259
8. BAI, J. and NG, S. (2013). Principal components estimation and identification of static factors. J. Econometrics 176 18-29. MR3067022
9. BICKEL, P. J. and LEVINA, E. (2008). Covariance regularization by thresholding. Ann. Statist. 36 2577-2604. MR2485008
10. BREITUNG, J. and PIGORSCH, U. (2009). A canonical correlation approach for selecting the number of dynamic factors. Oxford Bulletin of Economics and Statistics 75 23-36.
11. BREITUNG, J. and TENHOFEN, J. (2011). GLS estimation of dynamic factor models. J. Amer. Statist. Assoc. 106 1150-1166. MR2894771
12. BRILLINGER, D. R. (1981). Time Series: Data Analysis and Theory, 2nd ed. Holden-Day, Oakland, CA. MR0595684
13. CAI, T. T., MA, Z. and WU, Y. (2013). Sparse PCA: Optimal rates and adaptive estimation. Ann. Statist. 41 3074-3110. MR3161458
14. CANDÈS, E. J. and RECHT, B. (2009). Exact matrix completion via convex optimization. Found. Comput. Math. 9 717-772. MR2565240
15. CHEN, X. (2007). Large sample sieve estimation of semi-nonparametric models. In Handbook of Econometrics 76. North Holland, Amsterdam.
16. CONNOR, G., HAGMANN, M. and LINTON, O. (2012). Efficient semiparametric estimation of the Fama-French model and extensions. Econometrica 80 713-754. MR2951947
17. CONNOR, G. and LINTON, O. (2007). Semiparametric estimation of a characteristic-based factor model of stock returns. Journal of Empirical Finance 14 694-717.
18. DESAI, K. H. and STOREY, J. D. (2012). Cross-dimensional inference of dependent high-dimensional data. J. Amer. Statist. Assoc. 107 135-151. MR2949347
19. EFRON, B. (2010). Correlated z-values and the accuracy of large-scale statistical estimates. J. Amer. Statist. Assoc. 105 1042-1055. MR2752597
20. FAN, J., HAN, X. and GU, W. (2012). Estimating false discovery proportion under arbitrary covariance dependence. J. Amer. Statist. Assoc. 107 1019-1035. MR3010887
21. FAN, J., LIAO, Y. and MINCHEVA, M. (2013). Large covariance estimation by thresholding principal orthogonal complements. J. R. Stat. Soc. Ser. B. Stat. Methodol. 75 603-680. MR3091653
22. FAN, J., LIAO, Y. and SHI, X. (2015). Risks of large portfolios. J. Econometrics 186 367-387. MR3343792
23. FAN, J., LIAO, Y. and WANG, W. (2015). Supplement to "Projected principal component analysis in factor models." DOI:10.1214/15-AOS1364SUPP.
24. FORNI, M. and LIPPI, M. (2001). The generalized dynamic factor model: Representation theory. Econometric Theory 17 1113-1141. MR1867540
25. FORNI, M., HALLIN, M., LIPPI, M. and REICHLIN, L. (2000). The generalized dynamic-factor model: Identification and estimation. Rev. Econom. Statist. 82 540-554.
26. FORNI, M., HALLIN, M., LIPPI, M. and ZAFFARONI, P. (2015). Dynamic factor models with infinite-dimensional factor spaces: One-sided representations. J. Econometrics 185 359-371. MR3311826
27. FRIGUET, C., KLOAREG, M. and CAUSEUR, D. (2009). A factor model approach to multiple testing under dependence. J. Amer. Statist. Assoc. 104 1406-1415. MR2750571
28. HALLIN, M. and LIŠKA, R. (2007). Determining the number of factors in the general dynamic factor model. J. Amer. Statist. Assoc. 102 603-617. MR2325115
29. JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295-327. MR1863961
30. JUNG, S. and MARRON, J. S. (2009). PCA consistency in high dimension, low sample size context. Ann. Statist. 37 4104-4130. MR2572454
31. KOLTCHINSKII, V., LOUNICI, K. and TSYBAKOV, A. B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Statist. 39 2302-2329. MR2906869
32. LAM, C. and YAO, Q. (2012). Factor modeling for high-dimensional time series: Inference for the number of factors. Ann. Statist. 40 694-726. MR2933663
33. LEEK, J. T. and STOREY, J. D. (2008). A general framework for multiple testing dependence. Proc. Natl. Acad. Sci. USA 105 18718-18723.
34. LI, G., YANG, D., NOBEL, A. B. and SHEN, H. (2015). Supervised singular value decomposition and its asymptotic properties. J. Multivariate Anal. To appear.
35. LORENTZ, G. G. (1986). Approximation of Functions, 2nd ed. Chelsea Publishing, New York. MR0917270
36. MA, Z. (2013). Sparse principal component analysis and iterative thresholding. Ann. Statist. 41 772-801. MR3099121
37. NEGAHBAN, S. and WAINWRIGHT, M. J. (2011). Estimation of (near) low-rank matrices with noise and high-dimensional scaling. Ann. Statist. 39 1069-1097. MR2816348
38. NEWEY, W. K. and WEST, K. D. (1987). A simple, positive semidefinite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55 703-708. MR0890864
39. PARK, B. U., MAMMEN, E., HÄRDLE, W. and BORAK, S. (2009). Time series modelling with semiparametric factor dynamics. J. Amer. Statist. Assoc. 104 284-298. MR2504378
40. PAUL, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 1617-1642. MR2399865
41. SHEN, D., SHEN, H. and MARRON, J. S. (2013). Consistency of sparse PCA in high dimension, low sample size contexts. J. Multivariate Anal. 115 317-333. MR3004561
42. SHEN, D., SHEN, H., ZHU, H. and MARRON, J. (2013). Surprising asymptotic conical structure in critical sample eigen-directions. Technical report, Univ. North Carolina.
43. STOCK, J. H. and WATSON, M. W. (2002). Forecasting using principal components from a large number of predictors. J. Amer. Statist. Assoc. 97 1167-1179. MR1951271
44. VERSHYNIN, R. (2012). Introduction to the non-asymptotic analysis of random matrices. In Compressed Sensing 210-268. Cambridge Univ. Press, Cambridge. MR2963170