On Adaptive confidence Ellipsoids for sparse high dimensional linear models

Xiaoyang Xie

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arXiv · 2310.15659

On Adaptive confidence Ellipsoids for sparse high dimensional linear models

Xiaoyang Xie

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Abstract

In high-dimensional linear models the problem of constructing adaptive confidence sets for the full parameter is known to be generally impossible. We propose re-weighted loss functions under which constructing fully adaptive confidence sets for the parameter is shown to be possible. We give necessary and sufficient conditions on the weights for adaptive confidence sets to exist, and exhibit a concrete rate-optimal procedure in the feasible regime.

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Xiaoyang Xie. 2023-10-24. On Adaptive confidence Ellipsoids for sparse high dimensional linear models. https://arxiv.org/abs/2310.15659

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