Subjective Error and Non-expected Utility

通过这个研究项目，我完成了一篇题为“主观误差测量”的论文。我将解释它的动机和结果。符合Savage公理的决策者可以看作是通过求解一个统计推理问题来评价每一个行为，其中估计误差用误差平方损失函数来度量。然而，从决策者自己的偏好中推导出损失函数以及效用指数和主观概率是更可取的。我弱化萨维奇的公理来描述基于损失最小化的偏好，即决策者通过解决一个统计推理问题来评估每一个行为，其中估计误差是由一些可能不同于平方误差损失函数的损失函数来衡量的。此外，本文还提供了两个基于损失最小化的偏好示例，其损失函数比平方误差损失函数更通用。

As a result of this research program, I completed a paper entitled "Subjective error measure." I will explain its motivation and results. The decision-maker who complies with Savage's axioms can be regarded as evaluating each act by solving a statistical inference problem, in which the estimation error is measured by the squared-error loss function. However, it is more desirable to derive a loss function, as well as the utility index and the subjective probability, from the decision-maker's own preference. I weaken Savage's axioms to characterize the preference which is based on the loss-minimization in the sense that the decision-maker evaluates each act by solving a statistical inference problem, in which the estimation error is measured by some loss function which may be different from the squared-error loss function. Also, the paper provides two examples of preferences which are based on the loss-minimization with the loss function more general than the squared-error loss function.