Abstract

Title: Deep Statistical Learning for Nonlinear Semiparametric Regression: Post-Shrinkage, Weak Signals, and Sparsity
Abstract:
Nonlinear semiparametric regression provides a flexible framework for modelling complex relationships while retaining interpretable parametric components. Estimation and prediction become particularly challenging when models involve numerous covariates, sparse coefficient structures, and weak signals that may be overlooked by conventional variable-selection and shrinkage procedures. This paper considers post-shrinkage strategies for nonlinear semiparametric regression, emphasizing the distinction between strong, weak, and negligible effects. By combining shrinkage-based model selection with subsequent estimation, the methodology seeks to improve estimation accuracy and predictive performance while preserving scientifically meaningful information. Particular attention is given to the interplay between model complexity, signal strength, and the trade-off between estimation bias and variability. The suggested techniques are applied to gene expression data from 272 breast cancer patients in the United States, involving 1,566 potential explanatory variables, to illustrate their practical relevance in high-dimensional biomedical modelling. This application highlights the utility of post-shrinkage strategies for refining model specification and addressing the challenges of nonlinear relationships, sparsity, and heterogeneous signal strengths. Overall, the work emphasizes the role of principled statistical learning in developing interpretable and reliable nonlinear semiparametric regression models.