Goldberg, Yair; Song, Rui; Kosorok, Michael R. Adaptive \(Q\)-learning. (English) Zbl 1325.62073 Banerjee, M. (ed.) et al., From probability to statistics and back: high-dimensional models and processes. A Festschrift in honor of Jon A. Wellner. Including papers from the conference, Seattle, WA, USA, July 28–31, 2010. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-83-6). Institute of Mathematical Statistics Collections 9, 150-162 (2013). Summary: Developing an effective multi-stage treatment strategy over time is one of the essential goals of modern medical research. Developing statistical inference, including constructing confidence intervals for parameters, is of key interest in studies applying dynamic treatment regimens. Estimation and inference in this context are especially challenging due to non-regularity caused by the non-smoothness of the problem in the parameters. While various bootstrap methods have been proposed, there is a lack of theoretical validation for most bootstrap inference methods. Recently, R. Song et al. [Stat. Sin. 25, No. 3, 901–920 (2015; Zbl 1415.62054)] proposed the penalized \(Q\)-learning procedure, that enables valid inference without the need of bootstrapping. As a major drawback, penalized \(Q\)-learning can only handle discrete covariates. To overcome this issue, we propose an adaptive \(Q\)-learning procedure which is an adaptive version of penalized \(Q\)-learning. We show that the proposed method can not only handle continuous covariates, but it can also be more efficient than penalized \(Q\)-learning.For the entire collection see [Zbl 1319.62002]. Cited in 2 Documents MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62F12 Asymptotic properties of parametric estimators Keywords:adaptive estimation; dynamic treatment regimes; penalized estimation; \(Q\)-learning Citations:Zbl 1415.62054 PDFBibTeX XMLCite \textit{Y. Goldberg} et al., Inst. Math. Stat. Collect. 9, 150--162 (2013; Zbl 1325.62073) Full Text: DOI