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Selective inference with unknown variance via the square-root lasso

Author

Listed:
  • Xiaoying Tian
  • Joshua R Loftus
  • Jonathan E Taylor

Abstract

SummaryThere has been much recent work on inference after model selection in situations where the noise level is known. However, the error variance 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 inference for selected coefficients and the noise level simultaneously. The square-root lasso has the property that the choice of a reasonable tuning parameter does not depend on the noise level in the data. We provide valid $p$-values and confidence intervals for coefficients after variable selection and estimates for the model-specific variance. Our estimators perform better in simulations than other estimators of the noise variance. These results make inference after model selection significantly more applicable.

Suggested Citation

  • Xiaoying Tian & Joshua R Loftus & Jonathan E Taylor, 2018. "Selective inference with unknown variance via the square-root lasso," Biometrika, Biometrika Trust, vol. 105(4), pages 755-768.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:4:p:755-768.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy045
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    Citations

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    Cited by:

    1. Sean Jewell & Paul Fearnhead & Daniela Witten, 2022. "Testing for a change in mean after changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1082-1104, September.
    2. Markus Pelger & Jiacheng Zou, 2022. "Inference for Large Panel Data with Many Covariates," Papers 2301.00292, arXiv.org, revised Mar 2023.
    3. Andrea C. Garcia‐Angulo & Gerda Claeskens, 2023. "Exact uniformly most powerful postselection confidence distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 358-382, March.

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