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

This paper addresses the challenge of estimating high-dimensional parameters in non-standard data environments, where traditional methods often falter due to issues such as heavy-tailed distributions, data contamination, and dependent observations. We propose robust subsampling techniques, specifically Adaptive Importance Sampling (AIS) and Stratified Subsampling, designed to enhance the reliability and efficiency of parameter estimation. Under some clearly outlined conditions, we establish consistency and asymptotic normality for the proposed estimators, providing non-asymptotic error bounds that quantify their performance. Our theoretical foundations are complemented by controlled experiments demonstrating the superiority of our methods over conventional approaches. By bridging the gap between theory and practice, this work offers significant contributions to robust statistical estimation, paving the way for advancements in various applied domains.