robust against misspecification of the baseline function. This property is shared by A-learning. Third, empirical results from our comprehensive numerical study suggest favorable performance of the new robust regression estimator.

The rest of the paper is organized as follows. In Section 2, we first review the classical Q- and A- learning methods. Then we propose the new procedure and method and discuss its connection with existing methods. In Section 3, we study and prove the asymptotic properties of the proposed method, including consistency and asymptotic normality. In Section 4, a comprehensive numerical study is conducted to assess finite sample performance of the new procedure. In Section 5, we apply the method to ACTG175 data. Concluding remarks are given in Section 6. Throughout the paper, we use upper case letters to denote random variables and lower case letters to denote their values.

New Optimal Treatment Estimation Framework: Robust Regression
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Basic Notations and Assumptions
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For simplicity, we consider a single stage randomized clinical trial with two treatments. For each patient, the observed data is $({{\bm X}},A,Y)$, where ${{\bm X}}\in\mathcal{X}={\mathrm{I \! R} \mathit{^{p}}}$ denotes the baseline covariates, $A\in\mathcal{A}=\{0,1\}$ denotes the treatment assigned to the patient, and $Y$ is the real-valued response, 