Bai Jushan author Columbia University. Economics Shi Shuzhong author Columbia University. Economics originator contributor text Working papers New York Department of Economics, Columbia University 2011 Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed. Economic theory 1112-03 http://hdl.handle.net/10022/AC:P:11064 English NNC NNC 2011-09-01 14:57:26 -0400 2011-09-01 15:01:17 -0400 5066 eng