The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the...

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking...

We propose a novel technique to boost the power of testing a high-dimensional vector $H:\theta=0$ against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due...

Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely...

This article provides a selective overview of the recent developments in factor models and their applications in econometric learning. We focus on the perspective of the low-rank structure of factor models and particularly draw attention to estimating the model from the low-rank recovery point...