4,756
Views
187
CrossRef citations to date
0
Altmetric
Theory and Methods

Exact Post-Selection Inference for Sequential Regression Procedures

Pages 600-620 | Received 01 Oct 2014, Published online: 18 Aug 2016

References

  • Berk, R., Brown, L., Buja, A., Zhang, K., and Zhao, L. (2013), “Valid Post-Selection Inference,” Annals of Statistics, 41, 802–837.
  • Buhlmann, P. (2013), “Statistical Significance in High-Dimensional Linear Models,” Bernoulli, 19, 1212–1242.
  • Buja, A., and Brown, L. (2014), “Discussion: A Significance Test for the Lasso,” Annals of Statistics, 42, 509–517.
  • Choi, Y., Taylor, J., and Tibshirani, R. (2014), “Selecting the Number of Principal Components: Estimation of the True Rank of a Noisy Matrix,” arXiv: 1410.8260.
  • Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” Annals of Statistics, 32, 407–499.
  • Fithian, W., Sun, D., and Taylor, J. (2014), “Optimal Inference After Model Selection,” arXiv: 1410.2597.
  • Fithian, W., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2016), “Selective Sequential Model Selection,” arXiv:1512.02565.
  • G’Sell, M., Wager, S., Chouldechova, A., and Tibshirani, R. (2016), “Sequential Selection Procedures and False Discovery Rate Control,” Journal of the Royal Statistical Society, Series B, 78, 423--444.
  • Javanmard, A., and Montanari, A. (2014a), “Confidence Intervals and Hypothesis Testing for High-dimensional Regression,” Journal of Machine Learning Research, 15, 2869--2909.
  • Javanmard, A. (2014b), “Hypothesis Testing in High-dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory,” IEEE Transactions on Information Theory, 60, 6522--6554.
  • Lee, J., Sun, D., Sun, Y., and Taylor, J. (2016), “Exact Post-Selection Inference With the Lasso,” Annals of Statistics, 44, 907--927.
  • Lee, J., and Taylor, J. (2014), “Exact Post Model Selection Inference for Marginal Screening,” Advances in Neural Information Processing Systems, 27, 136--144.
  • Lehmann, E., and Romano, J. (2005), Testing Statistical Hypotheses (3rd ed.), New York: Springer.
  • Lockhart, R., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2014), “A Significance Test for the Lasso,” Annals of Statistics, 42, 413–468.
  • Loftus, J., and Taylor, J. (2014), “A Significance Test for Forward Stepwise Model Selection,” arXiv: 1405.3920.
  • Meinshausen, N., and Buhlmann, P. (2010), “Stability Selection,” Journal of the Royal Statistical Society, Series B, 72, 417–473.
  • Minnier, J., Tian, L., and Cai, T. (2011), “A Perturbation Method for Inference on Regularized Regression Estimates,” Journal of the American Statistical Association, 106, 1371–1382.
  • Reid, S., Taylor, J., and Tibshirani, R. (2014), “Post-selection Point and Interval Estimation of Signal Sizes in Gaussian Samples,” arXiv: 1405.3340.
  • Tibshirani, R. J. (2013), “The Lasso Problem and Uniqueness,” Electronic Journal of Statistics, 7, 1456–1490.
  • van de Geer, S., Buhlmann, P., Ritov, Y., and Dezeure, R. (2014), “On Asymptotically Optimal Confidence Regions and Tests for High-dimensional Models,” Annals of Statistics, 42, 1166–1201.
  • Wasserman, L., and Roeder, K. (2009), “High-Dimensional Variable Selection,” Annals of Statistics, 37, 2178–2201.
  • Zhang, C.-H., and Zhang, S. (2014), “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models,” Journal of the Royal Statistical Society, Series B, 76, 217–242.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.