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The minimum covariance determinant estimator for interval-valued data

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Abstract

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.

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Funding

This work was supported by the National Natural Science Foundation of China (Nos. 72071008) and the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), Ministry of Education.

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Authors and Affiliations

  1. School of Economics and Management, Beihang University, Beijing, 100191, China

    Wan Tian & Zhongfeng Qin

  2. Key Laboratory of Complex System Analysis, Management and Decision (Beihang University), Beijing, 100191, China

    Zhongfeng Qin

  3. Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), Ministry of Education, Shanghai, China

    Wan Tian

Authors
  1. Wan Tian
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  2. Zhongfeng Qin
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Contributions

WT Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing original draft. ZQ Conceptualization, Methodology, Validation, Supervision,Writing-review & editing.

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Correspondence to Zhongfeng Qin.

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Tian, W., Qin, Z. The minimum covariance determinant estimator for interval-valued data. Stat Comput 34, 80 (2024). https://doi.org/10.1007/s11222-024-10386-9

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