3 research outputs found
Rejoinder: Post Selection Shrinkage Estimation for High Dimensional Data Analysis
One fundamental ingredient of our work is to formally split the signals into strong and weak ones. The rationale is that the usual one-step method such as the least absolute shrinkage and selection operator (LASSO) may be very effective in detecting strong signals while failing to identify some weak ones, which in turn has a significant impact on the model fitting, as well as prediction. The discussions of both Fan and QYY contain very interesting comments on the separation of the three sets of variables. Regarding Assumption (A2) about the weak signal set S2, we admit that the original version was not as rigorous as it could have been, as it could have contained the variables in S3. We now propose the following Assumption (A2') that replaces (A2) in the original paper
Classification with Ultrahigh-Dimensional Features
Although much progress has been made in classification with high-dimensional
features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014},
classification with ultrahigh-dimensional features, wherein the features much
outnumber the sample size, defies most existing work. This paper introduces a
novel and computationally feasible multivariate screening and classification
method for ultrahigh-dimensional data. Leveraging inter-feature correlations,
the proposed method enables detection of marginally weak and sparse signals and
recovery of the true informative feature set, and achieves asymptotic optimal
misclassification rates. We also show that the proposed procedure provides more
powerful discovery boundaries compared to those in \citet{CaiSun:2014} and
\citet{JJin:2009}. The performance of the proposed procedure is evaluated using
simulation studies and demonstrated via classification of patients with
different post-transplantation renal functional types