The minimum covariance determinant estimator for interval-valued data

Effective estimation of covariance matrices is crucial for statistical analyses and applications. In this paper, we focus on the robust estimation of covariance matrix for interval-valued data in low and moderately high dimensions. In the low-dimensional scenario, we extend the Minimum Covariance Determinant (MCD) estimator to interval-valued data. We derive an iterative algorithm for computing this estimator, demonstrate its convergence, and theoretically establish that it retains the high breakdown-point property of the MCD estimator. Further, we propose a projection-based estimator and a regularization-based estimator to extend the MCD estimator to moderately high-dimensional settings, respectively. We propose efficient iterative algorithms for solving these two estimators and demonstrate their convergence properties. We conduct extensive simulation studies and real data analysis to validate the finite sample properties of these proposed estimators.