Adaptive and Stratified Subsampling Techniques for High Dimensional Non-Standard Data Environments

In the era of big data, researchers and practitioners across various domains are grappling with datasets of unprecedented scale and complexity. These high-dimensional datasets, characterized by a large number of features relative to the sample size, pose significant challenges to traditional statistical methods. Simultaneously, the increasing prevalence of non-standard data environments, such as those with heavy-tailed distributions or complex dependence structures, further complicates the landscape of data analysis. Subsampling techniques have emerged as a promising approach to address the computational challenges associated with large-scale data analysis. By working with a carefully chosen subset of the data, these methods aim to achieve a balance between statistical accuracy and computational efficiency. However, the theoretical foundations of subsampling in high-dimensional, nonstandard environments remain inadequately explored, leaving a critical gap in our understanding of their statistical properties and practical applicability.