On Cumulative Slicing Estimation for High Dimensional Data
On Cumulative Slicing Estimation for High Dimensional Data
复制标题
高维数据的累积切片估计
DOI：
10.5705/ss.202018.0381
复制
发表时间：
--
影响因子：
1.4
通讯作者：
Liping Zhu
中科院分区：
文献类型：
--
作者：
Cheng Wang;Zhou Yu;Liping Zhu
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 non-linear 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 highor 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 highand 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 → 0, where p stands for the covariate dimension and n stands for the sample size. If we make certain sparsity assumpStatistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)
