Uniform inference in high-dimensional Gaussian graphical models

Sven Klaassen, Jannis Kück, Martin Spindler and Victor Chernozhukov
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Sven Klaassen: Institute for Fiscal Studies
Jannis Kück: Institute for Fiscal Studies
Martin Spindler: Institute for Fiscal Studies

No CWP29/19, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models with the number of target parameters d being possible much larger than sample size. This is in particular important when certain features or structures of a causal model should be recovered. Our results highlight how in high-dimensional settings graphical models can be estimated and recovered with modern machine learning methods in complex data sets. To construct simultaneous con?dence regions on many target parameters, su?ciently fast estimation rates of the nuisance functions are crucial. In this context, we establish uniform estimation rates and sparsity guarantees of the square-root estimator in a random design under approximate sparsity conditions that might be of independent interest for related problems in high-dimensions. We also demonstrate in a comprehensive simulation study that our procedure has good small sample properties.

Date: 2019-06-12
New Economics Papers: this item is included in nep-big and nep-ore
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Related works:
Journal Article: Uniform inference in high-dimensional Gaussian graphical models (2023)
Working Paper: Uniform Inference in High-Dimensional Gaussian Graphical Models (2018)
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