What question did this study set out to answer?

The study aims to develop an adaptive estimator for partially linear regression models that handles high-dimensional data effectively.

April 30, 2026Turkiye Klinikleri Journal of Biostatistics0 citationsOpen Access

Estimation of Semiparametric Regression Model for High-Dimensional Data via Iterative Supervised Principal Components: Methodological Study

EYErsin YILMAZ

Key Points

The study aims to develop an adaptive estimator for partially linear regression models that handles high-dimensional data effectively.
Utilized B-spline profiling to address the nonparametric component
Applied iterative supervised component extraction from profiled residuals
Constructed adaptive importance weights and performed sparse estimation using LASSO
Achieved the lowest mean squared prediction error of 1.522 under Toeplitz correlation for 1000 predictors
Showed a false positive rate of 0.025, indicating improved control
Demonstrated about 12% lower prediction error compared to LASSO-PLM on the Riboflavin dataset

Abstract

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.

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