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Abstract:
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In this talk, I will propose a dimension reduction method to estimate the conditional average treatment effects based on observational data with multivariate confounders. This method can reduce the curse of dimensionality as much as possible while keeping the non- parametric merit. To impute potential outcomes in a more stable way, a nonparametric regression with prior dimension reduction is further used. This procedure leads to better es- timates than existing methods in finite sample, such as naive matching method and inverse propensity score weighting, and we demonstrated this phenomenon in our simulation studies. Further, we showed that the asymptotic variance of estimated central mean subspace is not involved in the asymptotic distribution of estimated conditional average treatment effects. According to this finding, we propose a more effective bootstrapping procedure without bootstrapping the estimated central mean subspace to estimate the asymptotic variances and make valid inference.
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