Double penalized variable selection for high-dimensional partial linear mixed effects models

In this study, we address the selection of both fixed and random effects in partial linear mixed effects models. By combining B-spline and QR decomposition techniques, we propose a double-penalized likelihood procedure for both estimating and selecting these effects. Furthermore, we introduce an orthogonality-based method to estimate the non-parametric component, ensuring that the fixed and random effects are separated without any mutual interference. The asymptotic properties of the resulting estimators are investigated under mild conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. Finally, we demonstrate the practical applicability of our methodology by analyzing a real data.