Objective: This study considers estimation in the partially linear regression model (PLM) with a high-dimensional linear component (p>>n), where estimation becomes difficult in the presence of nonlinear effects and correlated predictors. The aim is to develop a profiling-based adaptive estimator that extends iterative supervised principal components to the semiparametric PLM setting and uses the resulting dense estimates to construct adaptive penalty weights. Material and Methods: The proposed Adaptive Iterative Supervised Principal Components (ISPC)-PLM method consists of 4 steps: (1) B-splinebased profiling to remove the nonparametric component, (2) iterative supervised component extraction from the profiled residuals, (3) construction of adaptive importance weights, and (4) final sparse estimation via weighted Least Absolute Shrinkage and Selection Operator (LASSO). Monte Carlo simulations with 1,000 replications were performed under independence, Toeplitz, and block correlation structures. The proposed method was compared with LASSO-PLM, Smoothly Clipped Absolute Deviation-PLM, and Principal Component Analysis+LASSO-PLM. A real-data application was conducted using the Riboflavin production dataset. Results: The results indicate that Adaptive ISPC-PLM performs particularly well under multicollinearity, providing improved false-positive control and competitive prediction accuracy. Under Toeplitz correlation (p=1000), it achieved the lowest mean squared prediction error (1.522) and false positive rate (0.025). On the Riboflavin dataset, it produced about 12% lower prediction error than LASSO-PLM. Conclusion: Adaptive ISPC-PLM is a useful approach for highdimensional PLMs with moderate to strong predictor correlation.
Ersin YILMAZ (Thu,) studied this question.