Unrestricted and Controlled Identification of Loss Functions: Possibility and Impossibility Results
2019/02/26
研討會日期 : 2019-02-26
時間 : 14:30
主講人 : Professor Robert Lieli
主持人 : Professor Yu-Chin Hsu
地點 : Conference Room C103
演講者簡介 : Professor Lieli received his Ph.D. in Economics from University of California at San Diego in 2004. He is currently an Associate Professor at Central European University, Budapest. His research field is Econometrics.
演講摘要 : The property that the conditional mean is the unrestricted optimal forecast characterizes the Bregman class of loss functions; the property that the α-quantile is the unrestricted optimal forecast characterizes the generalized -piecewise linear (α-GPL) class. However, in settings where the forecaster's choice of forecasts is limited to the support of the predictive distribution, different Bregman losses lead to different forecasts. This is not true for the α-GPL class---the failure of identification is more fundamental. Motivated by these examples, we state simple conditions that can be used to ascertain if loss functions that are consistent for the same statistical functional become identifiable when off-support forecasts are disallowed. We also study the identifying power of unrestricted forecasts within the class of smooth, convex loss functions. For any such loss ⅇ, the set of losses consistent for the same statistical functional as ⅇ is a tiny subset of this class in a precise mathematical sense. Finally, we illustrate the identification problem posed by the non-uniqueness of consistent losses for moment based loss function estimation methods proposed in the literature.
