Group inference in high dimensions with applications to hierarchical testing


Date

2021

Publication Type

Journal Article

ETH Bibliography

yes

Citations

Altmetric

Data

Abstract

High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local heritability. Group inference in regression models can be measured with respect to a weighted quadratic functional of the regression sub-vector corresponding to the group. Asymptotically unbiased estimators of these weighted quadratic functionals are constructed and a novel procedure using these estimators for inference is proposed. We derive its asymptotic Gaussian distribution which enables the construction of asymptotically valid confidence intervals and tests which perform well in terms of length or power. The proposed test is computationally efficient even for a large group, statistically valid for any group size and achieving good power performance for testing large groups with many small regression coefficients. We apply the methodology to several interesting statistical problems and demonstrate its strength and usefulness on simulated and real data.

Publication status

published

Editor

Book title

Volume

15 (2)

Pages / Article No.

6633 - 6676

Publisher

Cornell University

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

debiasing Lasso; Heterogeneous effects; interaction test; local heritability; partial regression

Organisational unit

03502 - Bühlmann, Peter L. / Bühlmann, Peter L. check_circle

Notes

Funding

786461 - Statistics, Prediction and Causality for Large-Scale Data (EC)

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