A method of multi-dimensional variable selection for additive partial linear models.

What the paper says

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection.This study introduces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least absolute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD).These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to ensure sparse and interpretable models.The performance of both methods is evaluated through simulations using the mean squared error and variable selection criteria, assessing the correct detection of zero coefficients and the false omission of nonzero coefficients.A practical application involving financial data from the Baghdad Soft Drinks Company demonstrates their utility in identifying key predictors of stock market value.The results indicate that MAVE-SCAD performs well in high-dimensional and complex scenarios, whereas MAVE-ALASSO is better suited to small samples, producing more parsimonious models.These results highlight the effectiveness of these two methods in addressing key challenges in semiparametric modeling.