Open Access
2016 Robust learning for optimal treatment decision with NP-dimensionality
Chengchun Shi, Rui Song, Wenbin Lu
Electron. J. Statist. 10(2): 2894-2921 (2016). DOI: 10.1214/16-EJS1178


In order to identify important variables that are involved in making optimal treatment decision, Lu, Zhang and Zeng (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the misspecification of the conditional mean model. Two problems arise: (i) in a world of explosively big data, effective methods are needed to handle ultra-high dimensional data set, for example, with the dimension of predictors is of the non-polynomial (NP) order of the sample size; (ii) both the propensity score and conditional mean models need to be estimated from data under NP dimensionality.

In this paper, we propose a robust procedure for estimating the optimal treatment regime under NP dimensionality. In both steps, penalized regressions are employed with the non-concave penalty function, where the conditional mean model of the response given predictors may be misspecified. The asymptotic properties, such as weak oracle properties, selection consistency and oracle distributions, of the proposed estimators are investigated. In addition, we study the limiting distribution of the estimated value function for the obtained optimal treatment regime. The empirical performance of the proposed estimation method is evaluated by simulations and an application to a depression dataset from the STAR∗D study.


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Chengchun Shi. Rui Song. Wenbin Lu. "Robust learning for optimal treatment decision with NP-dimensionality." Electron. J. Statist. 10 (2) 2894 - 2921, 2016.


Received: 1 November 2015; Published: 2016
First available in Project Euclid: 13 October 2016

zbMATH: 06643255
MathSciNet: MR3557316
Digital Object Identifier: 10.1214/16-EJS1178

Keywords: Non-concave penalized likelihood , optimal treatment strategy , oracle property , Variable selection

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.10 • No. 2 • 2016
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