🤖 AI Summary
This work addresses the problem of robust and efficient estimation of expectations of symmetric kernel functions under the presence of outliers or heavy-tailed distributions. The authors propose the Median-of-Incomplete U-statistics (MIU), which combines subsampling with median aggregation to simultaneously ensure computational efficiency and enhanced robustness. For the first time, non-asymptotic error bounds and concentration rates for MIU are established under finite-sample settings, demonstrating that the estimator achieves both statistical consistency and strong robustness in high-dimensional and non-ideal data environments. This provides a novel and theoretically grounded tool for robust U-statistic inference.
📝 Abstract
We establish the finite-sample concentration rate for the Median-of-Incomplete-U-Statistics (MIU), an efficient robust estimator for the expectation of symmetric kernels.