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Activity Number: 617 - Testing
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract #306850
Title: Inference Without Compatibility
Author(s): Michael Law* and Ya'acov Ritov
Companies: University of Michigan and university of michigan
Keywords: Exponential weights; Linear models; Inference; Compatibility

We consider hypothesis testing problems for a single covariate in the context of a linear model with Gaussian design when p>n. Under minimal sparsity conditions of their type and without any compatibility condition, we construct an asymptotically Gaussian estimator with variance equal to the oracle least-squares. The estimator is based on a weighted average of all models of a given sparsity level in the spirit of exponential weighting. We adapt this procedure to estimate the signal strength and provide a few applications. We support our results using numerical simulations based on algorithm which approximates the theoretical estimator and provide a comparison with the de-biased lasso.

Authors who are presenting talks have a * after their name.

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