Maximum Likelihood Estimation and Inference for High Dimensional Nonlinear Factor Models with Application to Factor-Augmented Regressions

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.