Maximum Likelihood Estimation and Inference for High Dimensional Generalized Factor Models with Application to Factor-augmented Regressions

This paper reestablishes the main results in Bai (2003) and Bai and Ng(2006) for generalized factor models, with slightly stronger conditions on therelative magnitude of N(number of subjects) and T(number of time periods).Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mildconditions that allow for linear, Logit, Probit, Tobit, Poisson and some othersingle-index nonlinear models. The probability density/mass function is allowed to vary across subjects and time, thus mixed models are also allowed for.For factor-augmented regressions, this paper establishes the limit distributionsof the parameter estimates, the conditional mean, and the forecast when factorsestimated from nonlinear/mixed data are used as proxies for the true factors