Fiducial selector: Fast and efficient inference for high-dimensional regression

This paper presents the fiducial selector, an innovative inference method tailored for high-dimensional linear regression. Developed within the generalized fiducial inference (GFI) framework, this method incorporates a high-performance de-biasing component that significantly enhances the accuracy of the inference results. From a theoretical perspective, the fiducial selector guarantees model selection consistency and generates unbiased estimates of the significant parameters. On the practical front, this method is not only straightforward to implement and computationally efficient, but also provides reliable inference outcomes. Comparative analyses reveal that the fiducial selector tends to provide superior empirical performance in both statistical and computational efficiency compared to existing methods. With its strong theoretical foundation, fast computational speed, and superior empirical performance, the fiducial selector emerges as a highly effective and promising tool for practitioners and researchers working with complex, high-dimensional datasets.