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Robust learning for optimal treatment decision with NP-dimensionality

Shi, Chengchun, Song, Rui and Lu, Wenbin (2016) Robust learning for optimal treatment decision with NP-dimensionality. Electronic Journal of Statistics, 10 (2). 2894 - 2921. ISSN 1935-7524

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Identification Number: 10.1214/16-EJS1178

Abstract

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.

Item Type: Article
Official URL: https://projecteuclid.org/info/euclid.ejs
Additional Information: © 2016 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 15 Oct 2019 12:42
Last Modified: 27 Jan 2020 11:24
URI: http://eprints.lse.ac.uk/id/eprint/102114

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