Abstract:
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Standard theory in regression analysis has been plagued by the vulnerability of stringent model assumptions in the high dimensional setting, and the resulting inference often fails to take into account the modeling error. I will introduce a new inference framework for predictive regression inference. The proposed method is a generic tool that converts any point estimator to an interval predictor, producing prediction bands with valid average coverage under essentially no assumptions, while retaining the optimality of the initial point estimator under standard assumptions. Our method features a distinct out-of-sample fitting step, which explicitly incorporates future data points at which prediction is wanted. The generality and flexibility of this framework will be illustrated through several topics in regression analysis, including in-sample prediction, variable importance measure, and prediction with heteroskedastic error.
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