基于MRCD估计的多元线性回归模型的稳健估计

doi:10.16088/j.issn.1001-6600.2021060911

摘要/Abstract

摘要： 含异常值的数据和高维数据越来越频繁地出现,对现有的稳健估计和多元线性回归估计方法提出了挑战。传统的多元线性回归模型估计对异常值非常敏感,基于MCD估计方法的多元线性回归估计对异常值有一定的抵御作用。但随着数据维数的增加,MCD估计的精度不断降低,稳健性也随之降低,且当数据维数大于样本量时MCD估计方法失效。因此,本文利用MRCD的均值向量和协方差矩阵估计,提出了基于MRCD估计方法的高维稳健多元线性回归模型估计。数值模拟的结果表明,基于MRCD估计方法的多元线性回归模型估计能很好地抵御异常值,且在数据维数大于样本量的情况下,基于MRCD估计方法的多元线性回归估计更为有效。实证分析的结果表明,基于MRCD方法的多元线性回归估计能更好地抵御异常值并得到更好的预测效果。

关键词: 异常值, 高维数据, MCD估计, MRCD估计, 多元线性回归模型

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

中图分类号:

O212.1

颜海波, 邓罡, 姜云卢. 基于MRCD估计的多元线性回归模型的稳健估计[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 175-186.

YAN Haibo, DENG Gang, JIANG Yunlu. Robust Estimation of Multivariate Linear Regression Model Based on MRCD Estimation[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 175-186.

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