  This paper makes a selective survey on the recent development of the factor
model and its application on statistical learnings. We focus on the perspective
of the low-rank structure of factor models, and particularly draws attentions
to estimating the model from the low-rank recovery point of view. The survey
mainly consists of three parts: the first part is a review on new factor
estimations based on modern techniques on recovering low-rank structures of
high-dimensional models. The second part discusses statistical inferences of
several factor-augmented models and applications in econometric learning
models. The final part summarizes new developments dealing with unbalanced
panels from the matrix completion perspective.
