CIRJE-F-906 "Optimal Ridge-type Estimators of Covariance Matrix in High Dimension"
Author Name

Kubokawa, Tatsuya and Muni S. Srivastava

Date October 2013
Full Paper   PDF file

The problem of estimating the covariance matrix of normal and non-normal distributions is addressed when both the sample size and the dimension of covariance matrix tend to in nity. In this paper, we consider a class of ridge-type estimators which are linear combinations of the unbiased estimator and the identity matrix multiplied by a scalor statistic, and we derive a leading term of their risk functions relative to a quadratic loss function. Within this class, we obtain the optimal ridge-type estimator by minimizing the leading term in the risk approximation. It is interesting to note that the optimal weight is based on a statistic for testing sphericity of the covariance matrix.