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Abstract:
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We consider high dimensional partial linear models, where the dimension of parametric components is allowed to be exponentially high w.r.t. sample size. We propose a semiparametric version of de-biased lasso estimator. In the high dimensional regime, this new estimate is shown to be asymptotically normal and achieve the semiparametric efficiency bound. Based on this distributional result, we further conduct simultaneous hypothesis testing. Interesting applications such as support recovery and multiple testing with family-wise error rate control will also be discussed.
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