Title: Integrating regularized covariance matrix estimators
Authors: Phoenix Feng - London School of Economics (United Kingdom) [presenting]
Clifford Lam - London School of Economics and Political Science (United Kingdom)
Abstract: When the dimension $p$ is close to or even larger than the sample size $n$, regularizing the sample covariance matrix is the key to obtaining a satisfactory covariance matrix estimator. One branch of regularization assumes specific structures for the true covariance matrix $\Sigma_0$. Another one regularizes on the eigenvalues directly without structure assumptions. The former makes sense when one is confident in a specific structure, while the latter is sound when no specific structures are known. Under more a practical scenario where one is not certain of which regularization method to use, we introduce an integration covariance matrix estimator which is a linear combination of a rotation-equivariant estimator and a regularized covariance matrix estimator assuming a specific structure for $\Sigma_0$. We estimate the weights in the linear combination and show that they asymptotically go to the true underlying weights. To generalize, we can put two regularized estimators into the linear combination, each assumes a specific structure for $\Sigma_0$. We demonstrate the superior performance of our estimator when compared to other state-of-the-art estimators through extensive simulation studies and real data analyses.