# Simultaneous estimation of normal means with side information

## TL;DR

This paper develops a data-driven method for estimating normal means using side information, improving accuracy in high-dimensional settings and demonstrating its application in gene expression data integration.

## Contribution

It introduces an asymptotically optimal, data-driven decision rule for normal mean estimation leveraging side information, with applications in genomics.

## Key findings

- The proposed rule asymptotically achieves the minimum possible risk.
- It can outperform existing methods in numerical experiments.
- Demonstrated effectiveness in integrating gene expression datasets.

## Abstract

The integrative analysis of multiple datasets is an important strategy in data analysis. It is increasingly popular in genomics, which enjoys a wealth of publicly available datasets that can be compared, contrasted, and combined in order to extract novel scientific insights. This paper studies a stylized example of data integration for a classical statistical problem: leveraging side information to estimate a vector of normal means. This task is formulated as a compound decision problem, an oracle integrative decision rule is derived, and a data-driven estimate of this rule based on minimizing an unbiased estimate of its risk is proposed. The data-driven rule is shown to asymptotically achieve the minimum possible risk among all separable decision rules, and it can outperform existing methods in numerical properties. The proposed procedure leads naturally to an integrative high-dimensional classification procedure, which is illustrated by combining data from two independent gene expression profiling studies.