A novel residual subsampling method for skew-normal mode regression model with massive data

With the advent of big data, the fields of biomedicine and economics generate massive data with skew characteristics. Numerous methods have been proposed for modeling either skewed or massive data, whereas most existing methods cannot allow a direct handling of massive and skewed data. We first investigate the subsampling algorithms for skew-normal mode regression model, which include uniform subsampling, leverage subsampling, optimal subsampling, and vector mode subsampling. Since the aforementioned algorithms mainly leverage the value of the information module to calculate the sampling probability without accounting for the residuals in the modeling process. This observation motivates us to propose a novel residual subsampling method with applications to massive data. We then employ the signal-to-noise ratio (SNR) to carry out simulation studies to compare the performance of various sampling methods under various information quantities. Finally, a real-data example is provided for illustrative methods.