Discovering differential genes through the detection of outliers in samples from disease group subjects is a new and important approach for gene expression analysis. Extending the outlier mean of Chen et al. (2010a), we develop the asymptotic distributions of the outlier least squares estimator (LSE) and the outlier proportion for the linear regression model. An optimal property of the best linear outlier mean acting as an outlier estimator version of the Gauss–Markov theorem for the outlier LSE is presented. Power comparisons demonstrate that tests based on outlier estimators are competitive in detecting a shift of the parent tail distribution. An analysis of DNA microarray data from samples of pancreatic breast tumors supports the use of outlier-based methods.