Project Euclid

References

• Benjamini, Y., Heller, R. and Yekutieli, D. (2009). Selective inference in complex research. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 367 4255–4271.
  Mathematical Reviews (MathSciNet): MR2546387
  Digital Object Identifier: doi:10.1098/rsta.2009.0127
  
• Benjamini, Y. and Yekutieli, D. (2005). False discovery rate-adjusted multiple confidence intervals for selected parameters. J. Amer. Statist. Assoc. 100 71–93.
  Mathematical Reviews (MathSciNet): MR2156820
  Digital Object Identifier: doi:10.1198/016214504000001907
  
• Berk, R., Brown, L., Buja, A., Zhang, K. and Zhao, L. (2013). Valid post-selection inference. Ann. Statist. 41 802–837.
  Mathematical Reviews (MathSciNet): MR3099122
  Digital Object Identifier: doi:10.1214/12-AOS1077
  Project Euclid: euclid.aos/1369836961
  
• Cox, D. R. (1975). A note on data-splitting for the evaluation of significance levels. Biometrika 62 441–444.
  Mathematical Reviews (MathSciNet): MR378189
  Digital Object Identifier: doi:10.1093/biomet/62.2.441
  
• Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. Ann. Statist. 32 407–499.
  Mathematical Reviews (MathSciNet): MR2060166
  Digital Object Identifier: doi:10.1214/009053604000000067
  Project Euclid: euclid.aos/1083178935
  
• Fisher, R. (1956). On a test of significance in Pearson’s Biometrika Tables (No. 11). J. Roy. Statist. Soc. Ser. B. 18 56–60.
  Mathematical Reviews (MathSciNet): MR82773
  
• Fithian, W., Sun, D. and Taylor, J. (2014). Optimal inference after model selection. Preprint. Available at arXiv:1410.2597.
  arXiv: 1410.2597
  
• Javanmard, A. and Montanari, A. (2013). Confidence intervals and hypothesis testing for high-dimensional regression. Preprint. Available at arXiv:1306.3171.
  arXiv: 1306.3171
  
• Knight, K. and Fu, W. (2000). Asymptotics for lasso-type estimators. Ann. Statist. 28 1356–1378.
  Mathematical Reviews (MathSciNet): MR1805787
  Digital Object Identifier: doi:10.1214/aos/1015957397
  Project Euclid: euclid.aos/1015957397
  
• Leeb, H. and Pötscher, B. M. (2005). Model selection and inference: Facts and fiction. Econometric Theory 21 21–59.
  Mathematical Reviews (MathSciNet): MR2153856
  Digital Object Identifier: doi:10.1017/S0266466605050036
  
• Leeb, H. and Pötscher, B. M. (2006). Can one estimate the conditional distribution of post-model-selection estimators? Ann. Statist. 34 2554–2591.
  Mathematical Reviews (MathSciNet): MR2291510
  Digital Object Identifier: doi:10.1214/009053606000000821
  Project Euclid: euclid.aos/1169571807
  
• Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses, 3rd ed. Springer, New York.
  Mathematical Reviews (MathSciNet): MR2135927
  
• Lockhart, R., Taylor, J., Tibshirani, R. and Tibshirani, R. (2014). A significance test for the lasso (with discussion). Ann. Statist. 42 413–468.
  Mathematical Reviews (MathSciNet): MR3210970
  Digital Object Identifier: doi:10.1214/13-AOS1175
  Project Euclid: euclid.aos/1400592161
  
• Miller, A. (2002). Subset Selection in Regression, 2nd ed. Chapman & Hall/CRC, Boca Raton, FL.
  Mathematical Reviews (MathSciNet): MR2001193
  
• Negahban, S. N., Ravikumar, P., Wainwright, M. J. and Yu, B. (2012). A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers. Statist. Sci. 27 538–557.
  Mathematical Reviews (MathSciNet): MR3025133
  Digital Object Identifier: doi:10.1214/12-STS400
  Project Euclid: euclid.ss/1356098555
  
• Pötscher, B. M. (1991). Effects of model selection on inference. Econometric Theory 7 163–185.
  Mathematical Reviews (MathSciNet): MR1128410
  Digital Object Identifier: doi:10.1017/S0266466600004382
  
• Pötscher, B. M. and Schneider, U. (2010). Confidence sets based on penalized maximum likelihood estimators in Gaussian regression. Electron. J. Stat. 4 334–360.
  Mathematical Reviews (MathSciNet): MR2645488
  Digital Object Identifier: doi:10.1214/09-EJS523
  Project Euclid: euclid.ejs/1268655653
  
• Robinson, G. K. (1979). Conditional properties of statistical procedures. Ann. Statist. 7 742–755.
  Mathematical Reviews (MathSciNet): MR532239
  Digital Object Identifier: doi:10.1214/aos/1176344725
  Project Euclid: euclid.aos/1176344725
  
• Sampson, A. R. and Sill, M. W. (2005). Drop-the-losers design: Normal case. Biom. J. 47 257–268.
  Mathematical Reviews (MathSciNet): MR2145117
  Digital Object Identifier: doi:10.1002/bimj.200410119
  
• Sill, M. W. and Sampson, A. R. (2009). Drop-the-losers design: Binomial case. Comput. Statist. Data Anal. 53 586–595.
  Mathematical Reviews (MathSciNet): MR2654594
  
• Storey, J. D. (2003). The positive false discovery rate: A Bayesian interpretation and the $q$-value. Ann. Statist. 31 2013–2035.
  Mathematical Reviews (MathSciNet): MR2036398
  Digital Object Identifier: doi:10.1214/aos/1074290335
  Project Euclid: euclid.aos/1074290335
  
• Taylor, J., Lockhart, R., Tibshirani, R. J. and Tibshirani, R. (2014). Post-selection adaptive inference for least angle regression and the lasso. Preprint. Available at arXiv:1401.3889.
  arXiv: 1401.3889
  
• Tian, X. and Taylor, J. (2015). Asymptotics of selective inference. Preprint. Available at arXiv:1501.03588.
  arXiv: 1501.0358
  
• Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
  Mathematical Reviews (MathSciNet): MR1379242
  
• Tibshirani, R. J. (2013). The lasso problem and uniqueness. Electron. J. Stat. 7 1456–1490.
  Mathematical Reviews (MathSciNet): MR3066375
  Digital Object Identifier: doi:10.1214/13-EJS815
  Project Euclid: euclid.ejs/1369148600
  
• Tibshirani, R. J., Rinaldo, A., Tibshirani, R. and Wasserman, L. (2015). Uniform asymptotic inference and the bootstrap after model selection. Preprint. Available at arXiv:1506.06266.
  arXiv: 1506.0626
  
• van de Geer, S., Bühlmann, P., Ritov, Y. and Dezeure, R. (2013). On asymptotically optimal confidence regions and tests for high-dimensional models. Preprint. Available at arXiv:1303.0518.
  arXiv: 1303.0518
  Mathematical Reviews (MathSciNet): MR3070248
  Digital Object Identifier: doi:10.1016/j.jspi.2013.03.006
  
• Weinstein, A., Fithian, W. and Benjamini, Y. (2013). Selection adjusted confidence intervals with more power to determine the sign. J. Amer. Statist. Assoc. 108 165–176.
  Mathematical Reviews (MathSciNet): MR3174610
  Digital Object Identifier: doi:10.1080/01621459.2012.737740
  
• Zhang, C.-H. and Zhang, S. S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 217–242.
  Mathematical Reviews (MathSciNet): MR3153940
  Digital Object Identifier: doi:10.1111/rssb.12026
  
• Zhong, H. and Prentice, R. L. (2008). Bias-reduced estimators and confidence intervals for odds ratios in genome-wide association studies. Biostatistics 9 621–634.
  Mathematical Reviews (MathSciNet): MR2712234
  
• Zollner, S. and Pritchard, J. K. (2007). Overcoming the winner’s curse: Estimating penetrance parameters from case-control data. Am. J. Hum. Genet. 80 605–615.
• Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B. Stat. Methodol. 67 301–320.
  Mathematical Reviews (MathSciNet): MR2137327
  Digital Object Identifier: doi:10.1111/j.1467-9868.2005.00503.x