概率统计讨论班

报告题目: High-Dimensional Cumulant Tensor Inference: Statistical–Computational Limits and Gains from Bandability

报告人：韩岳峰（美国圣母大学）

时   间：2026年7月23日（星期四），下午16:00-17:00

地 点：海纳苑2幢820

摘要：Higher-order cumulants capture non-Gaussian dependence beyond covariance, but their estimation is challenging in high dimensions. In the first part of this talk, I discuss the statistical and computational limits of estimating and detecting cumulant tensors under the tensor spectral norm. The minimax estimation rate is $\sqrt{p/n}\wedge 1$, while natural sample cumulants can be suboptimal for orders $d\ge3$. I also describe an unusual gap between computationally efficient estimation and detection. In the second part, I introduce bandable cumulant tensors for ordered data and a tapered estimator whose performance depends on an effective bandwidth rather than the ambient dimension. I conclude with an application to higher-order Yule–Walker equations for non-Gaussian autoregressive models.

联系人：庞天晓（txpang@zju.edu.cn）