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B0562
Title: Robust learning for optimal treatment decision with NP-dimensionality Authors:  Rui Song - North Carolina State University (United States) [presenting]
Abstract: In order to identify important variables that are involved in making optimal treatment decision, a penalized least squared regression framework for a fixed number of predictors has been previously proposed 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 the NP dimensionality. We propose a two-step estimation procedure for deriving the optimal treatment regime under the 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.