Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (1): 175-186.doi: 10.16088/j.issn.1001-6600.2021060911

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Robust Estimation of Multivariate Linear Regression Model Based on MRCD Estimation

YAN Haibo1, DENG Gang2, JIANG Yunlu2*   

  1. 1. School of Public Administration, Jinan University, Guangzhou Guangdong 510632, China;
    2. School of Economics, Jinan University, Guangzhou Guangdong 510632, China
  • Received:2021-06-09 Revised:2021-07-18 Online:2022-01-25 Published:2022-01-24

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Abstract: Data with outliers and high-dimensional data appear more and more frequently, challenging the existing robust estimation methods and multivariate linear model estimation methods. The traditional multivariate linear model estimation is very sensitive to outliers, and the multivariate linear model estimation based on the MCD estimation method has a certain resistance to outliers. But with the increase of the data dimensionality, the accuracy of MCD estimation continues to decrease, and the robustness also decreases. The MCD estimation method fails when the data dimensionality is greater than the sample size. Therefore, using the mean vector and covariance matrix estimation of MRCD, a high-dimensional robust multivariate linear model estimation based on the MRCD estimation method is proposed. Numerical simulation results show that the multivariate linear model estimation based on the MRCD estimation method can resist outliers well, and when the data dimension is larger than the sample size, the multivariate linear model estimation based on the MRCD estimation method is more effective. The results of empirical analysis show that the multiple linear regression estimation based on the MRCD method can better resist outliers and get better prediction results.

Key words: outliers, high-dimensional data, MCD estimation, MRCD estimation, multivariate linear model

CLC Number: 

  • O212.1
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