Seminar: Extrapolation-Aware Nonparametric Statistical Inference

Speaker: Niklas Pfister, University of Copenhagen

Time and place: Tuesday, September 24, 11:00, room SPs08, Copenhagen Business School (Solbjerg Pl. 3, 2000 Frederiksberg)

Title: Extrapolation-Aware Nonparametric Statistical Inference

Abstract We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. While extrapolating is straightforward in parametric models, it becomes challenging in nonparametric models. In this work, we extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions that can be combined with existing inference techniques to draw extrapolation-aware conclusions. The proposed class of extrapolation assumptions stipulate that the conditional function attains its minimal and maximal directional derivative, in each direction, within the observed support. We illustrate how the framework applies to several statistical applications including prediction and uncertainty quantification. We furthermore propose a consistent estimation procedure that can be used to adjust existing nonparametric estimates to account for extrapolation by providing lower and upper extrapolation bounds. The procedure is empirically evaluated on both simulated and real-world data.

For a detailed overview of planned future seminars at the section of Statistics, CBS, see https://www.cbs.dk/en/research/departments-and-centres/department-of-finance/center-statistics/seminars