A note on the asymptotic properties of least squares estimation in high dimensional constrained factor models

Constrained factor models proposed by Tsai and Tsay (2010) have wide potential applications. The existing asymptotic theory of the least squares estimator, however, falls short of asymptotic representations and limiting distributions, which limits the applicabilities. This paper fills this gap by explicitly giving the asymptotic representations and associated limiting distributions. Theoretical analysis indicates that the least square estimates are asymptotically biased. Bias-corrected estimators are therefore proposed. Monte Carlo simulations confirm our theoretical results.