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2015

Selective inference with unknown variance via the square-root LASSO

Tian, Xiaoying, Loftus, Joshua R., Taylor, Jonathan E.

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There has been much recent work on inference after model selection when the noise level is known, however, $\sigma$ is rarely known in practice and its estimation is difficult in high-dimensional settings.

In this work we propose using the square-root LASSO (also known as the scaled LASSO) to perform selective inference for the coefficients and the noise level simultaneously.
The square-root LASSO has the property that choosing a reasonable tuning parameter is scale-free, namely it does not depend on the noise level in the data.
We provide valid p-values and confidence intervals for the coefficients after selection, and estimates for model specific variance.

Selective inference with unknown variance via the square-root LASSO · Around

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Then

Tibshirani, R. J. (2013), ‘The lasso problem and uniqueness’, Electronic Journal of Statistics
Original
2013
Later among the works it cites.
arXiv: 1410.2597. http://arxiv.org/abs/1410.2597
Original
Fithian, W., Sun, D. & Taylor, J. (2014), ‘Optimal inference after model selection’, arXiv:1410.2597 [math, stat] · 2014
Later among the works it cites.
Taylor, J., Lockhart, R., Tibshirani, R. J. & Tibshirani, R. (2014), ‘Post-selection adaptive inference for least angle regression and the lasso’, arXiv:1401.3889 [stat]
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Later among the works it cites.
Barber, R. F. & Candes, E. J. (2016), ‘A knockoff filter for high-dimensional selective inference’, arXiv preprint arXiv:1602.03574
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2016
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