  The minimum covariance determinant (MCD) estimator is ubiquitous in
multivariate analysis, the critical step of which is to select a subset of a
given size with the lowest sample covariance determinant. The concentration
step (C-step) is a common tool for subset-seeking; however, it becomes
computationally demanding for high-dimensional data. To alleviate the
challenge, we propose a depth-based algorithm, termed as \texttt{FDB}, which
replaces the optimal subset with the trimmed region induced by statistical
depth. We show that the depth-based region is consistent with the MCD-based
subset under a specific class of depth notions, for instance, the projection
depth. With the two suggested depths, the \texttt{FDB} estimator is not only
computationally more efficient but also reaches the same level of robustness as
the MCD estimator. Extensive simulation studies are conducted to assess the
empirical performance of our estimators. We also validate the computational
efficiency and robustness of our estimators under several typical tasks such as
principal component analysis, linear discriminant analysis, image denoise and
outlier detection on real-life datasets. A R package \textit{FDB} and potential
extensions are available in the Supplementary Materials.
