High dimensional T-type Estimator for robust covariance matrix estimation with applications to elliptical factor models

In this paper, a regularized t-type estimator is proposed for high-dimensional scatter matrix estimation, where the number of dimensions p is comparable to, or even larger than the sample size n, and its thresholding form is employed to deal with sparse settings. Then, regularized t-type estimator is extended to high-dimensional elliptic factor models with outliers for robust identification of common factor numbers. Finally, we illustrate that the proposed regularized t-type estimator significantly outperforms the competitors through extensive simulations, even in cases with high-dimensional data. Meanwhile, the t-type estimator can significantly improve the efficiency of Tyler’s M-estimator in Goes et al. (Ann Stat 48(1):86–110, 2020) when the samples follow a possibly heavy-tailed elliptical distribution with a non-central or unknown location parameter.