Wang, Fa (2017): Maximum likelihood estimation and inference for high dimensional nonlinear factor models with application to factor-augmented regressions.
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Abstract
This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for high dimensional nonlinear factor models, with slightly stronger conditions on the relative magnitude of N(number of subjects) and T(number of time periods). Factors and loadings are estimated by maximum likelihood. Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear models, Logit, Probit, Tobit, Poisson and some other nonlinear models. The density function is allowed to vary across subjects, thus mixed models are explicitly allowed for. For factor-augmented regressions, this paper establishes the limit distributions of the parameter estimates, the conditional mean as well as the forecast when factors estimated from nonlinear/mixed data are used as proxies for the true factors.
Item Type: | MPRA Paper |
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Original Title: | Maximum likelihood estimation and inference for high dimensional nonlinear factor models with application to factor-augmented regressions |
English Title: | Maximum likelihood estimation and inference for high dimensional nonlinear factor models with application to factor-augmented regressions |
Language: | English |
Keywords: | Factor model, Discrete data, Maximum likelihood, High dimension, Factor-augmented regression, Forecasting |
Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C35 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions |
Item ID: | 93484 |
Depositing User: | Dr Fa Wang |
Date Deposited: | 20 May 2019 14:10 |
Last Modified: | 30 Sep 2019 10:23 |
References: | [1] Bai (2003): Inferential Theory for Factor Models of Large Dimensions, Econometrica, 71, 135-171. [2] Bai (2009): Panel Data Models with Interactive Fixed Effects, Econometrica, 77, 1229-1279. [3] Bai and Li (2012): Statistical Analysis of Factor Models of High Dimension, Annals of Statistics, 436-465. [4] Bai and Li (2016): Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension, Review of Economics and Statistics, 98, 298-309. [5] Bai and Ng (2002): Determining the Number of Factors in Approximate Factor Models, Econometrica, 70, 191-221. [6] Bai and Ng (2006): Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-augmented Regressions, Econometrica, 74, 1133-1150. [7] Bartholomew (1980): Factor Analysis for Categorical Data, Journal of the Royal Statistical Society. Series B, 293-321. [8] Bartholomew and Knott (1999): Latent Variable Models and Factor Analysis. Edward Arnold. [9] Bernanke, Boivin and Eliasz (2005): Measuring the Effects of Monetary Policy: A Factor-augmented Vector Autoregressive (FAVAR) approach, Quarterly Journal of Economics, 120, 387-422. [10] Bohning and Lindsay (1988): Monotonicity of Quadratic-approximation Algorithms, Annals of the Institute of Statistical Mathematics, 40, 641-663. [11] Campbell, Lo and Mackinlay (1997): The Econometrics of Financial Markets. New Jersey: Princeton University Press. [12] Chen (2016): Estimation of Nonlinear Panel Models with Multiple Unobserved Effects, Warwick Economics Research Paper Series. [13] Chen, Fernandez-Val and Weidner (2014): Nonlinear Panel Models with Inter- active Effects, arXiv preprint arXiv:1412.5647. [14] Chen, Fernandez-Val and Weidner (2018): Nonlinear Factor Models for Network and Panel Data, Cemmap Working Paper CWP38/18 [15] Collins, Dasgupta and Schapire (2001): A Generalization of Principal Component Analysis to the Exponential Family, Advances in Neural Information Processing System, Vol. 13. [16] Cox and Reid (1987): ìParameter Orthogonality and Approximate Conditional Inference, Journal of the Royal Statistical Society. Series B, 1-39. [17] Creal, Schwaab, Koopman and Lucas (2014): Observation-driven Mixed- measurement Dynamic Factor Models with an Application to Credit Risk, Review of Economics and Statistics, 96, 898-915. [18] de Leeuw (2006): Principal Component Analysis of Binary Data by Iterated Singular Value Decomposition, Computational Statistics & Data Analysis, 50, 21-39. [19] Feng, Wang, Han, Xia and Tu (2013): The Mean Value Theorem and Taylor's Expansion in Statistics, American Statistician, 67, 245-248. [20] Fernandez-Val and Weidner (2016): Individual and Time Effects in Nonlinear Panel Models with Large N, T, Journal of Econometrics, 192, 291-312. [21] Filmer and Pritchett (2001): Estimating Wealth Effects without Expenditure Data or Tears: An Application to Educational Enrollments in States of India, Demography, 38, 115-132. [22] Hahn and Newey (2004): Jackknife and Analytical Bias Reduction for Nonlinear Panel Models, Econometrica, 72, 1295n-1319. [23] Hahn and Kuersteiner (2011): Bias Reduction for Dynamic Nonlinear Panel Models with Fixed Effects, Econometric Theory, 27, 1152-1191. [24] Hunter and Lange (2004): A Tutorial on MM Algorithms, American Statistician, 58, 30-37. [25] Koopman and Lucas (2008): A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk, Journal of Business & Economic Statistics, 26, 510-525. [26] Koopman, Lucas and Monteiro (2008): The Multi-state Latent Factor Intensity Model for Credit Rating Transitions, Journal of Econometrics, 142, 399-424. [27] Koopman, Lucas and Schwaab (2011): Modeling Frailty-correlated Defaults Using Many Macroeconomic Covariates, Journal of Econometrics, 162, 312- 325. [28] Jennrich (1969): ìAsymptotic Properties of Non-linear Least Squares Estimators, The Annals of Mathematical Statistics, 40, 633-643. [29] Joreskog and Moustaki (2001): Factor Analysis of Ordinal Variables: A Com- parison of Three Approaches, Multivariate Behavioral Research, 36, 347-387. [30] Lancaster (2000): The Incidental Parameter Problem since 1948,î Journal of Econometrics, 95, 391-413. [31] Lancaster (2002): Orthogonal Parameters and Panel Data, Review of Economic Studies, 69, 647-666. [32] Lange, Hunter and Young (2000): Optimization Transfer Using Surrogate Objective Functions, Journal of Computational and Graphical Statistics, 9, 1-20. [33] McNeil and Wendin (2007): Bayesian Inference for Generalized Linear Mixed Models of Portfolio Credit Risk, Journal of Empirical Finance, 14, 131-149. [34] Moustaki (1996): A Latent Trait and a Latent Class Model for Mixed Observed Variables, British Journal of Mathematical and Statistical Psychology, 49, 313- 334. [35] Moustaki (2000): A Latent Variable Model for Ordinal Variables, Applied Psychological Measurement, 24, 211-223. [36] Moustaki and Knott (2000): Generalized Latent Trait Models, Psychometrika, 65, 391-411. [37] Newey and McFadden (1994): Large sample Estimation and Hypothesis Testing, Handbook of Econometrics, Vol. IV, 2111-2245. [38] Ng (2015): Constructing Common Factors from Continuous and Categorical Data, Econometric Reviews, 34, 1141-1171. [39] Ross (1976): The Arbitrage Theory of Capital Asset Pricing, Journal of Finance, 13, 341-360. [40] Schein, Saul and Ungar (2003): A Generalized Linear Model for Principal Component Analysis of Binary Data,Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics. [41] Schonbucher (2000): Factor Models for Portfolio Credit Risk, Bonn Econ Discussion Papers 16. [42] Stock and Watson (2002): Forecasting Using Principal Components from a Large Number of Predictors, Journal of American Statistical Association, 97, 1167-1179. [43] Stock and Watson (2016): Factor Models and Structural Vector Autoregressions in Macroeconomics, Handbook of Macroeconomics, forthcoming. [44] Wu (1981): Asymptotic Theory of Nonlinear Least Squares Estimation, The Annals of Statistics, 501-513. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/93484 |