Electronic Journal of Statistics

High-dimensional inference in misspecified linear models

Peter Bühlmann and Sara van de Geer

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We consider high-dimensional inference when the assumed linear model is misspecified. We describe some correct interpretations and corresponding sufficient assumptions for valid asymptotic inference of the model parameters, which still have a useful meaning when the model is misspecified. We largely focus on the de-sparsified Lasso procedure but we also indicate some implications for (multiple) sample splitting techniques. In view of available methods and software, our results contribute to robustness considerations with respect to model misspecification.

Article information

Electron. J. Statist., Volume 9, Number 1 (2015), 1449-1473.

Received: March 2015
First available in Project Euclid: 7 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J07: Ridge regression; shrinkage estimators
Secondary: 62F25: Tolerance and confidence regions

Confidence interval de-sparsified Lasso hypothesis test Lasso multiple sample splitting sparsity


Bühlmann, Peter; van de Geer, Sara. High-dimensional inference in misspecified linear models. Electron. J. Statist. 9 (2015), no. 1, 1449--1473. doi:10.1214/15-EJS1041. https://projecteuclid.org/euclid.ejs/1436277593

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