Abstract:
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Detection of treatment effect is frequently needed in treatment or policy evaluations. We consider the problem of treatment effect detection in the context of model selection when a large number of covariates are present and there are possible violations of the assumed link function, which is the functional form of the model which relates the outcome variable to the covariates and the random error. We allow the true link function to be completely arbitrary expect that y depends on covariates only though a linear combination of x. Under certain assumptions, the Lasso-type method under model misspecification is shown to have the sure screening property. However, it is generally invalid to perform data-driven model selection and derive statistical inference from the selected model. We adopt the idea of data splitting, where the number of variables is then reduced to a manageable size using the first split, while classical testing method under model misspecification can be applied to the remaining variables, using the data from the second split. Multiple random split is performed to reproduce the result and tame the erratic discontinuities of selection-based estimators.
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