Simultaneous estimation of normal means with side information

08/16/2019
by   Sihai Dave Zhao, et al.
0

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.

READ FULL TEXT

page 12

page 15

page 22

04/30/2022

A nonparametric regression approach to asymptotically optimal estimation of normal means

Simultaneous estimation of multiple parameters has received a great deal...
11/26/2019

On Optimal Solutions to Compound Statistical Decision Problems

In a compound decision problem, consisting of n statistically independen...
05/10/2020

A nonparametric empirical Bayes approach to covariance matrix estimation

We propose an empirical Bayes method to estimate high-dimensional covari...
11/17/2021

Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques

We study a new method for estimating the risk of an arbitrary estimator ...
11/25/2020

A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Star...
03/16/2019

Deciding with Judgment

A decision maker starts from a judgmental decision and moves to the clos...
10/31/2018

Solving multiple-criteria R&D project selection problems with a data-driven evidential reasoning rule

In this paper, a likelihood based evidence acquisition approach is propo...