1,506
Views
56
CrossRef citations to date
0
Altmetric
Theory and Methods

High-Dimensional Sparse Additive Hazards Regression

&
Pages 247-264 | Received 01 Aug 2011, Published online: 15 Mar 2013

REFERENCES

  • Andersen , P. K. and Gill , R. D. 1982 . “Cox’s Regression Model for Counting Processes: A Large Sample Study,” . The Annals of Statistics , 10 : 1100 – 1120 .
  • Antoniadis , A. , Fryzlewicz , P. and Letué , F. 2010 . “The Dantzig Selector in Cox’s Proportional Hazards Model,” . Scandinavian Journal of Statistics , 37 : 531 – 552 .
  • Bertsekas , D. P. 1999 . Nonlinear Programming (2nd ed.) , Belmont, MA : Athena Scientific .
  • Bradic , J. , Fan , J. and Jiang , J. 2011 . “Regularization for Cox’s Proportional Hazards Model With NP-Dimensionality,” . The Annals of Statistics , 39 : 3092 – 3120 .
  • Breheny , P. and Huang , J. 2011 . “Coordinate Descent Algorithms for Nonconvex Penalized Regression, With Applications to Biological Feature Selection,” . The Annals of Applied Statistics , 5 : 232 – 253 .
  • Breslow , N. E. and Day , N. E. 1987 . Statistical Models in Cancer Research, 2: The Design and Analysis of Cohort Studies , Lyon : IARC .
  • Cai , J. , Fan , J. , Li , R. and Zhou , H. 2005 . “Variable Selection for Multivariate Failure Time Data,” . Biometrika , 92 : 303 – 316 .
  • Cox , D. R. and Oakes , D. 1984 . Analysis of Survival Data , London : Chapman & Hall .
  • Daubechies , I. , Defrise , M. and De Mol , C. 2004 . “An Iterative Thresholding Algorithm for Linear Inverse Problems With a Sparsity Constraint,” . Communications on Pure and Applied Mathematics , 57 : 1413 – 1457 .
  • Dem’yanov , V. F. and Vasil’ev , L. V. 1985 . Nondifferentiable Optimization , New York : Springer .
  • Fan , J. 1997 . Comments on “Wavelets in Statistics: A Review,” by A. Antoniadis . Journal of the Italian Statistical Society , 6 : 131 – 138 .
  • Fan , J. and Fan , Y. 2008 . “High-Dimensional Classification Using Features Annealed Independence Rules,” . The Annals of Statistics , 36 : 2605 – 2637 .
  • Fan , J. and Li , R. 2001 . “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” . Journal of the American Statistical Association , 96 : 1348 – 1360 .
  • Fan , J. and Li , R. 2002 . “Variable Selection for Cox’s Proportional Hazards Model and Frailty Model,” . The Annals of Statistics , 30 : 74 – 99 .
  • Fan , J. and Lv , J. 2008 . “Sure Independence Screening for Ultrahigh Dimensional Feature Space” (with discussion) . Journal of the Royal Statistical Society, Series B , 70 : 849 – 911 .
  • Fan , J. and Lv , J. 2010 . “A Selective Overview of Variable Selection in High Dimensional Feature Space (invited review article),” . Statistica Sinica , 20 : 101 – 148 .
  • Fan , J. and Lv , J. 2011 . “Nonconcave Penalized Likelihood With NP-Dimensionality,” . IEEE Transactions on Information Theory , 57 : 5467 – 5484 .
  • Fan , J. , Lv , J. and Qi , L. 2011 . “Sparse High-Dimensional Models in Economics,” . Annual Review of Economics , 3 : 291 – 317 .
  • Friedman , J. , Hastie , T. , Höfling , H. and Tibshirani , R. 2007 . “Pathwise Coordinate Optimization,” . The Annals of Applied Statistics , 1 : 302 – 332 .
  • Fu , W. J. 1998 . “Penalized Regressions: The Bridge Versus the Lasso,” . Journal of Computational and Graphical Statistics , 7 : 397 – 416 .
  • Hoeffding , W. 1963 . “Probability Inequalities for Sums of Bounded Random Variables,” . Journal of the American Statistical Association , 58 : 13 – 30 .
  • Horn , R. A. and Johnson , C. R. 1985 . Matrix Analysis , New York : Cambridge University Press .
  • Jarrow , R. A. 2009 . “Credit Risk Models,” . Annual Review of Financial Economics , 1 : 37 – 68 .
  • Kosorok , M. R. 2008 . Introduction to Empirical Processes and Semiparametric Inference , New York : Springer .
  • Leng , C. , Lin , Y. and Wahba , G. 2006 . “A Note on the Lasso and Related Procedures in Model Selection,” . Statistica Sinica , 16 : 1273 – 1284 .
  • Leng , C. and Ma , S. 2007 . “Path Consistent Model Selection in Additive Risk Model via Lasso,” . Statistics in Medicine , 26 : 3753 – 3770 .
  • Lin , D. Y. and Ying , Z. 1994 . “Semiparametric Analysis of the Additive Risk Model,” . Biometrika , 81 : 61 – 71 .
  • Lv , J. and Fan , Y. 2009 . “A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares,” . The Annals of Statistics , 37 : 3498 – 3528 .
  • Martinussen , T. and Scheike , T. H. 2009 . “Covariate Selection for the Semiparametric Additive Risk Model,” . Scandinavian Journal of Statistics , 36 : 602 – 619 .
  • Massart , P. 2000 . “About the Constants in Talagrand’s Concentration Inequalities for Empirical Processes,” . The Annals of Probability , 28 : 863 – 884 .
  • Mazumder , R. , Friedman , J. H. and Hastie , T. 2011 . “SparseNet: Coordinate Descent With Nonconvex Penalties,” . Journal of the American Statistical Association , 106 : 1125 – 1138 .
  • Meinshausen , N. and Bühlmann , P. 2006 . “High-Dimensional Graphs and Variable Selection With the Lasso,” . The Annals of Statistics , 34 : 1436 – 1462 .
  • Meinshausen , N. and Bühlmann , P. 2010 . “Stability Selection” (with discussion) . Journal of the Royal Statistical Society, Series B , 72 : 417 – 473 .
  • Rosenwald , A. , Wright , G. , Chan , W. C. , Connors , J. M. , Campo , E. , Fisher , R. I. , Gascoyne , R. D. , Muller-Hermelink , H. K. , Smeland , E. B. and Staudt , L. M. 2002 . “The Use of Molecular Profiling to Predict Survival After Chemotherapy for Diffuse Large-B-Cell Lymphoma,” . The New England Journal of Medicine , 346 : 1937 – 1947 .
  • Tibshirani , R. 1996 . “Regression Shrinkage and Selection via the Lasso,” . Journal of the Royal Statistical Society, Series B , 58 : 267 – 288 .
  • Tibshirani , R. 1997 . “The Lasso Method for Variable Selection in the Cox Model,” . Statistics in Medicine , 16 : 385 – 395 .
  • van der Vaart , A. W. 1998 . Asymptotic Statistics , New York : Cambridge University Press .
  • van der Vaart , A. W. and Wellner , J. A. 1996 . Weak Convergence and Empirical Processes: With Applications to Statistics , New York : Springer .
  • Wainwright , M. J. 2009 . “Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using ℓ1-Constrained Quadratic Programming (Lasso),” . IEEE Transactions on Information Theory , 55 : 2183 – 2202 .
  • Wu , T. T. and Lange , K. 2008 . “Coordinate Descent Algorithms for Lasso Penalized Regression,” . The Annals of Applied Statistics , 2 : 224 – 244 .
  • Zhang , C.-H. 2010 . “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” . The Annals of Statistics , 38 : 894 – 942 .
  • Zhang , H. H. and Lu , W. 2007 . “Adaptive Lasso for Cox’s Proportional Hazards Model,” . Biometrika , 94 : 691 – 703 .
  • Zhao , P. and Yu , B. 2006 . “On Model Selection Consistency of Lasso,” . Journal of Machine Learning Research , 7 : 2541 – 2563 .
  • Zou , H. 2006 . “The Adaptive Lasso and Its Oracle Properties,” . Journal of the American Statistical Association , 101 : 1418 – 1429 .
  • Zou , H. 2008 . “A Note on Path-Based Variable Selection in the Penalized Proportional Hazards Model,” . Biometrika , 95 : 241 – 247 .
  • Zou , H. and Hastie , T. 2005 . “Regularization and Variable Selection via the Elastic Net,” . Journal of the Royal Statistical Society, Series B , 67 : 301 – 320 .
  • Zou , H. and Li , R. 2008 . “One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models” (with discussion) . The Annals of Statistics , 36 : 1509 – 1566 .

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.