Expectile Regression with Reciprocal Lassopenalty
Abstract
Expectile regression (ER) has emerged as a valuable alternative to quantile regression, offering robust modeling of the conditional distribution of response variables across diverse fields such as economics, medicine, and ecology. While traditional penalized ER models like SCAD, elastic-net, and adaptive Lasso improve variable selection, they often struggle with achieving optimal sparsity and precision. Existing penalties typically exhibit continuity and symmetry, which may not sufficiently penalize near-zero coefficients in high-dimensional data, limiting their effectiveness in variable selection. This study proposes a novel penalized expectile regression method using the reciprocal Lasso (rLasso) penalty, which introduces discontinuity at the origin and infinite shrinkage as coefficients approach zero. Simulation studies across various settings and error distributions demonstrate that ER-rLasso consistently achieves the lowest root mean square error (RMSE) and false positive rate (FPR), outperforming established ER models. In real-data analysis involving prostate cancer, ER-rLasso showed superior predictive accuracy across all tested expectile levels. The distinct penalization structure of rLasso, being non-symmetric and non-convex, introduces a more aggressive variable selection mechanism that enhances model sparsity and interpretability.
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