Sufficient dimension reduction with additional information

TL;DR

This paper introduces a two-stage dimension reduction method that leverages additional correlated information to improve inference about the relationship between response and covariates, enhancing efficiency and accuracy.

Contribution

It proposes a novel two-stage dimension reduction approach that incorporates extra information from variable W to improve inference about (Y,X).

Findings

Better separation of patient survival groups in breast cancer data.

Fewer components needed for diabetes classification with higher accuracy.

Improved efficiency in statistical inference using the proposed method.

Abstract

Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable $W$ that is strongly correlated with $Y$. From a statistical point of view, making inference about $(Y,X)$ without using $W$ will lose efficiency. However, it is not trivial to incorporate the information of $W$ to infer $(Y,X)$. In this article, we propose a two-stage dimension reduction method for $(Y,X)$, that is able to utilize the additional information from $W$. The main idea is to confine the searching space, by constructing an envelope subspace for the target of interest. In the analysis of breast cancer data, the risk score constructed from the two-stage method can well separate patients with different survival experiences. In the Pima data, the two-stage method requires fewer components to infer the diabetes status, while achieving higher classification accuracy than conventional method.