How well can we learn large factor models without assuming strong factors?

Understand

In this paper, we consider the problem of learning models with a latent factor structure.

• The focus is to find what is possible and what is impossible if the usual strong factor condition is not imposed.
• We study the minimax rate and adaptivity issues in two problems: pure factor models and panel regression with interactive fixed effects.
• For pure factor models, if the number of factors is known, we develop adaptive estimation and inference procedures that attain the minimax rate.