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On Cumulative Slicing Estimation for High Dimensional Data
时间  Datetime
2017-05-12 14:00 — 15:00 
地点  Venue
Large Conference Room
报告人  Speaker
朱利平教授
单位  Affiliation
中国人民大学统计与大数据研究院
邀请人  Host
王成
报告摘要  Abstract

In the context of sufficient dimension reduction (SDR), sliced inverse regression (SIR) is the first and perhaps one of the most popular tools to reduce the covariate dimension for high dimensional nonlinear regressions. Despite the fact that the performance of SIR is very insensitive to the number of slices when the covariate is low or moderate dimensional, our empirical studies indicate that, the performance of SIR relies heavily upon the number of slices when the covariate is high or ultrahigh dimensional.  How to select the optimal number of slices for SIR is still a longstanding problem in the SDR literature, which is a crucial issue for SIR to be effective in high and ultrahigh dimensional regressions.

 In this paper, we work with an improved version of SIR, the cumulative slicing estimation (CUME) method, which does not require selecting the optimal number of slices. We provide a general framework to analyze the phase transition phenomenon for the CUME method.  We show that, without sparsity assumption, CUME is consistent if and only if $p/n\to 0$, where $p$ stands for the covariate dimension and $n$ stands for the sample size. If we make certain sparsity assumptions, then the thresholding estimate for the CUME method is consistent as long as $\log(p)/n\to0$.  We demonstrate the superior performance of our proposals through extensive numerical experiments.

嘉宾介绍:

朱利平,中国人民大学统计与大数据研究院教授、博士生导师。国家自然科学基金优秀青年基金获得者,入选中组部万人计划青年拔尖人才计划以及教育部新世纪优秀人才计划等。主要研究领域包括高维及超高维数据统计分析、半参数回归模型统计推断、充分性降维等。在统计学四大顶级期刊发表论文十多篇,其他重要SCI论文五十余篇,其中多篇论文被列为统计学领域ESI高被引论文。