Parameter selection and application on the smoothly clipped absolute deviation method
Qiqiang Yang, Xuemin Zi · 2022 3rd International Conference on Computer Vision, Image and Deep Learning & International Conference on Computer Engineering and Applications (CVIDL & ICCEA) · 2022
With the development of science and technology, high-dimensional data has become a popular topic in scientific research. However, most variables are meaningless in high-dimensional data. Therefore, the sparsity problem in high-dimensional data is worth to be focus in the statistical methodology and application in decades. Smoothly clipped absolute deviation (SCAD) method is often used to solve the problem of high-dimensional variable selection. The selection of regular parameters is obtained by generalized cross-validation, and the coordinate descent algorithm is often used to estimate the model coefficients in the past. In this paper, AIC and BIC are used to find the optimal regularization parameters, and the path calibration sparse shooting algorithm is used to estimate the model coefficients. Our algorithm has a strong guarantee in theory. We can achieve global linear convergence to the only sparse local optimal, and the convergence speed is fast. It is found that residual sum of squares of model obtained by path calibration sparse shooting algorithm combined with BIC, which is the smallest in solving SCAD problem by numerical experiments.