题目：On A Phase Transition in General Order Spline Regression

主讲人：华盛顿大学 韩放助理教授

主持人：统计学院 常晋源教授

时间：2020年7月17日（周五）10:00-11:20

直播平台及会议ID：腾讯会议，131 504 931

报告提要：

In the Gaussian sequence model, we study the fundamental limit of approximating the signal by a class of (generalized) splines with free knots. Our results give the minimax rate of estimation and reveal the corresponding phase transition. The transition boundary demonstrates the critical role of the order of differentiability at each inner knot in the separation between a faster loglog(16n) and a slower log(en) rate. We further show that, once encouraging an additional ‘d-monotonicity’ shape constraint (including monotonicity for d = 0 and convexity for d=1), the above phase transition is eliminated and the faster kloglog(16n/k) rate can be achieved for all k. These results provide theoretical support for developing L_0-penalized (shape-constrained) spline regression procedures as useful alternatives to L_1- and L_2-penalized ones.

主讲人简介：

Dr. Fang Han is an assistant professor of statistics at the University of Washington. He obtained his Ph.D. from the Department of Biostatistics, Johns Hopkins University in 2015. Previously, he received his B.S. (Mathematics) from Peking University and M.S. (Biostatistics) from University of Minnesota. His main methodology/theory interests lie in rank-based methods, nonparametric regression methods, and hierarchical models.