Simultaneous selection and inference for varying coefficients with zero regions: a soft-thresholding approach

Varying coefficient models have been used to explore dynamic effects in many scientific areas, such as in medicine, finance, and epidemiology. As most existing models ignore the existence of zero regions, we propose a new soft-thresholded varying coefficient model, where the coefficient functions are piecewise smooth with zero regions. Our new modeling approach enables us to perform variable selection, detect the zero regions of selected variables, obtain point estimates of the varying coefficients with zero regions, and construct a new type of sparse confidence intervals that accommodate zero regions. We prove the asymptotic properties of the estimator, based on which we draw statistical inference. Our simulation study reveals that the proposed sparse confidence intervals achieve the desired coverage probability. We apply the proposed method to analyze a large-scale preoperative opioid study.

Automated summary

Varying coefficient models with zero regions are proposed in this study. The new modeling approach allows for variable selection, detects zero regions, obtains point estimates of varying coefficients, and constructs sparse confidence intervals accommodating zero regions. The asymptotic properties of the estimator are proven for statistical inference. Simulation results show that the proposed sparse confidence intervals have desired coverage probability. The method is applied to analyze a large-scale preoperative opioid study.