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2014 On the uniform convergence of empirical norms and inner products, with application to causal inference
Sara van de Geer
Electron. J. Statist. 8(1): 543-574 (2014). DOI: 10.1214/14-EJS894

Abstract

Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to symmetrization. They also play a prominent role in statistical applications. The contraction inequality has been a main tool but recently other approaches have shown to lead to better results in important cases. We present an overview including the linear (anisotropic) case, and give new results for inner products of functions. Our main application will be the estimation of the parental structure in a directed acyclic graph. As intermediate result we establish convergence of the least squares estimator when the model is wrong.

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Sara van de Geer. "On the uniform convergence of empirical norms and inner products, with application to causal inference." Electron. J. Statist. 8 (1) 543 - 574, 2014. https://doi.org/10.1214/14-EJS894

Information

Published: 2014
First available in Project Euclid: 16 May 2014

zbMATH: 1348.62152
MathSciNet: MR3211024
Digital Object Identifier: 10.1214/14-EJS894

Subjects:
Primary: 62G08
Secondary: 60G50

Keywords: Additive model , Causal inference , empirical measure , Uniform convergence

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 1 • 2014
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