  This paper develops a general framework for estimation of high-dimensional
conditional factor models via nuclear norm regularization. We establish large
sample properties of the estimators, and provide an efficient computing
algorithm for finding the estimators as well as a cross validation procedure
for choosing the regularization parameter. The general framework allows us to
estimate a variety of conditional factor models in a unified way and quickly
deliver new asymptotic results. We apply the method to analyze the cross
section of individual US stock returns, and find that imposing homogeneity may
improve the model's out-of-sample predictability.
