## Electronic Journal of Statistics

### High-dimensional inference in misspecified linear models

#### Abstract

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

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

Dates
First available in Project Euclid: 7 July 2015

https://projecteuclid.org/euclid.ejs/1436277593

Digital Object Identifier
doi:10.1214/15-EJS1041

Mathematical Reviews number (MathSciNet)
MR3367666

Zentralblatt MATH identifier
1327.62420

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

#### Citation

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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