Advanced search
Publication Cover
Journal of the American Statistical Association Volume 114, 2019 - Issue 527
Submit an article Journal homepage
1,459
Views
7
CrossRef citations to date
0
Altmetric
Theory and Methods

Proper Inference for Value Function in High-Dimensional Q-Learning for Dynamic Treatment Regimes

Wensheng ZhuKey Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, ChinaView further author information
,
Donglin ZengDepartments of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NCView further author information
&
Rui SongDepartment of Statistics, North Carolina State University, Raleigh, NCView further author information
Pages 1404-1417 | Received 01 Apr 2017, Accepted 01 Jun 2018, Published online: 29 Oct 2018

References

  • Altman, T., and Leger, C. (1994), “Cross-validation, the Bootstrap, and Related Methods for Tuning Parameter Selection,” Technical Report, The Cornell University Library, 1–23.
  • Chakraborty, B., Laber, E., and Zhao, Y. (2013), “Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme,” Biometrics, 69, 714–723.
  • Chakraborty, B., and Moodie, E. E. M. (2013), Statistical Methods for Dynamic Treatment Regimes, New York: Springer.
  • Chakraborty, B., Murphy, S., and Strecher, V. (2010), “Inference for Non-Regular Parameters in Optimal Dynamic Treatment Regimes,” Statistical Methods in Medical Research, 19, 317–343.
  • 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 Lv, J. (2011), “Non-Concave Penalized Likelihood with NP-Dimensionality,” IEEE Transactions on Information Theory, 57, 5467–5484.
  • Fava, M., Rush, A. J., Trivedi, M. H., Nierenberg, A. A., Thase, M. E., Sackeim, H. A., Quitkin, F. M., Wisniewski, S., Lavori, P. W., Rosenbaum, J. F., and Kupfer, D. J. (2003), “Background and Rationale for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) Study,” Psychiatric Clinics of North America, 26, 457–494.
  • Laber, E., Lizotte, D., Qian, M., Pelham, W., and Murphy, S. (2014), “Dynamic Treatment Regimes: Technical Challenges and Applications,” Electronic Journal of Statistics, 8, 1225–1272.
  • Luedtke, A. R., and Van Der Laan, M. J. (2016), “Statistical Inference for the Mean Out- Come under a Possibly Non-Unique Optimal Treatment Strategy,” The Annals of Statistics, 44, 713–742.
  • 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.
  • Moodie, E., and Richardson, T. (2010), “Estimating Optimal Dynamic Regimes: Correcting Bias under the Null,” Scandinavian Journal of Statistics, 37, 126–146.
  • Qian, M., and Murphy, S. A. (2011), “Performance Guarantees for Individualized Treatment Rules,” Annals of Statistics, 39, 1180–1210.
  • Robins, J. M. (2004), “Optimal Structural Nested Models for Optimal Sequential Decisions,” in Proceedings of the Second Seattle Symposium in Biostatistics, Springer, pp. 189–326.
  • Rush, A. J., Fava, M., Wisniewski, S. R., Lavori, P. W., Trivedi, M. H., Sackeim, H. A., Thase, M. E., Nierenberg, A. A., Quitkin, F. M., Kashner, T. M., Kupfer, D. J., Rosenbaum, J. F., Alpert, J., Stewart, J. W., McGrath, P. J., Biggs, M. M., Shores-Wilson, K., Lebowitz, B. D., Ritz, L., and Niederehe, G. (2004), “Sequenced Treatment Alternatives to Relieve Depression (STAR*D): Rationale and Design,” Controlled Clinical Trials, 25, 119–142.
  • Song, R., Wang, W., Zeng, D., and Kosorok, M. R. (2015), “Penalized Q-Learning for Dynamic Treatment Regimens,” Statistica Sinica, 25, 901–920.
  • Watkins, C. J. (1989), “Learning from Delayed Rewards,” Ph.D. dissertation, University of Cambridge, England.
  • Zhang, C. (2010), “Nearly Unbiased Variable Selection under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.