Shrinkage Estimators for High-Dimensional Covariance Matrices

As high-dimensional data becomes ubiquitous, standard estimators of the population covariance matrix become difficult to use. Specifically, in the case where the number of samples is small (large p small n) the sample covariance matrix is not positive definite. In this paper we explore some recent estimators of sample covariance matrices in the large p, small n setting namely, shrinkage estimators. Shrinkage estimators have been shown to be positive definite and well-conditioned, two key properties to a good estimate of the population covariance matrix. We test how well the estimators preserve the qualitites of the population covariance matrix and how much information is retained from the sample covariace matrix. We also perform a simulation study to measure the difference between the estimators and the population covariance and compare the different estimators.