James-Stein shrinkage for high dimensional eigenvectors

Music City Center 

For a 1-factor model in high dimensions, we describe a shrinkage method that improves the sample estimate of the first principal component of the sample covariance matrix by a quantifiable amount. We prove asymptotic theorems when the dimension p tends to infinity while the number of samples n stays bounded. The improved estimator is shown to significantly improve the estimated minimum variance optimization problem subject to an arbitrary number of linear equality constraints. This is joint work with Lisa Goldberg and Hubeyb Gurdogan.