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Abstract:
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Estimating a treatment effect conditional on baseline covariates is a central goal of many statistical investigations. However, for nonparametric methods of estimating the treatment effect, if the dimension of the baseline covariates is large, implementation becomes difficult and sometimes infeasible due to the curse of dimensionality. Hence, sufficient dimension reduction of baseline covariates can be useful before estimating the treatment effect. Because our object of interest only involves the conditional mean treatment effect, the reduction is targeted to find a few linear combination of the covariates sufficient to estimate the treatment effect function. We refer to such a dimension reduction subspace as a central treatment effect subspace (CTES). The structural dimension of the CTES determines whether the treatment effect is heterogeneous in the population and therefore is useful in many applications. We propose methods to estimate the CTES and its structural dimension, investigate the theoretical properties of these estimators, and demonstrate their effectiveness with numerical studies.
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