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We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We first study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. This estimator is shown to have an asymptotic normal distribution. Furthermore, we verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultane
We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. T
Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment r
Capture-recapture (CRC) surveys are widely used to estimate the size of a population whose members cannot be enumerated directly. When $k$ capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a $2^k
Although parametric empirical Bayes confidence intervals of multiple normal means are fundamental tools for compound decision problems, their performance can be sensitive to the misspecification of the parametric prior distribution (typically normal