Regression analysis is a central methodology in statistics, and least squares estimation is the standard approach for estimating coefficients in linear regression models. Despite its optimality under ideal conditions, the least squares estimator is extremely sensitive to outliers and can be seriously distorted by even a single anomalous observation. To address this limitation, we propose trimmed estimators for multivariate linear regression coefficients. We study the fundamental properties of the proposed estimators and derive their asymptotic distributions. Using these results, we evaluate the asymptotic relative efficiency of the proposed estimators relative to the classical least squares estimator. The robustness of the estimators is further examined through their finite-sample breakdown points. The results demonstrate that the proposed estimators can provide very strong robustness against outliers while maintaining substantial efficiency.

Jin Wang is a professor of statistics at Northern Arizona University (NAU), USA. His main research areas include nonparametric multivariate analysis, biostatistics, reliability analysis, probabilistic risk analysis, change-point problems, and asymptotic theory. His contributions to nonparametric multivariate statistics include a nonparametric multivariate kurtosis measure (Wang and Serfling, 2005), a family of kurtosis orderings for multivariate distributions (Wang, 2009), a generalized spread function and a generalized multivariate kurtosis ordering (Wang and Zhou, 2012), a graphical method to compare spread and kurtosis of two multivariate data sets and a new graphical method to assess multivariate normality (Wang, 2019), and so on. Besides theoretical research, Wang is also interested in applications of statistics in various fields. He worked in industry for eight years (1991-1999) and worked on several health-related projects at NAU.