Robust variable selection with exponential squared loss for linear mixed-effects models

In this paper, we focus on the selection of fixed effects in linear mixed-effects models. To achieve robust variable selection, we propose a penalized exponential squared loss estimator, which is integrated with the QR decomposition technique. This procedure effectively separates the fixed and random effects, ensuring that they do not interfere with each other. Under certain regularity conditions, our proposed estimator demonstrates \(\sqrt{n}\) $\sqrt{n}$ -consistency and possesses the oracle property. To evaluate the finite sample performance of our estimator, we conduct extensive simulation studies. Additionally, we analyze a real data example to illustrate the practical application of our proposed procedure.