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High-dimensional inference in misspecified linear models. (English) Zbl 1327.62420

Summary: 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.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62F25 Parametric tolerance and confidence regions

Software:

PDCO; covTest; hdi
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Full Text: DOI arXiv Euclid

References:

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