Renewable ridge selection operator with streaming datasets

The dynamic nature of streaming data presents significant challenges to traditional offline methods that require collecting all data. In this paper, the issue of high correlation in streaming data is addressed by proposing a renewable ridge selection operator that incorporates individually penalized ridge regression for variable selection. Unlike traditional offline models, this method is adapted to real-time streaming data through renewable estimating equation and objective function. As data flows in, summary statistics that occupy a fixed amount of memory are continuously updated, reducing the dependence on storing the data during the analysis process. Theoretically, selection consistency is established, and this property holds true regardless of the number of data batches, indicating that our method is adaptive to scenarios where streaming data continuously arrive. Numerical results demonstrate that the proposed model effectively handles high correlation in streaming data, offering a robust method to variable selection and estimation. At last, our method is applied to analyze some real datasets for illustration.