Group inference in high dimensions with applications to hierarchical testing
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Author / Producer
Date
2021
Publication Type
Journal Article
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yes
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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.
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Publication status
published
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Book title
Journal / series
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.
Notes
Funding
786461 - Statistics, Prediction and Causality for Large-Scale Data (EC)