Adaptive Learning in Robust Linear Regression With a Semiparametric Skew‐Normal Scale Mixture Distribution

ABSTRACT The ordinary least squares method is commonly used for estimating regression coefficients for the linear regression. However, this approach is highly sensitive to influential outliers and loses efficiency when the error follows a skewed or heavy‐tailed distribution. To address these limitations, we propose the adoption of semiparametric skew‐normal scale mixture distributions for the error. By using a nonparametric maximum likelihood estimator for the scale factor in skew‐normal scale mixture, we can mitigate the risk of misspecification issues and produce robust estimators without any model selection procedure. Furthermore, we present simulation studies and real data analyses to demonstrate the performance of the proposed method.