Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error
观测误差下的变点、边界与前沿估计AI 解读 ↓
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观测误差下的变点、边界与前沿估计
- 研究问题
- 分布支撑边界或生产前沿受到观测误差污染时，如何减轻系统误差，误差分布未知又对可识别性有何限制？
- 方法与思路
- 作者提出降低观测误差影响的简单方法及进一步修正，同时讨论前沿估计的不适定性和误差分布未知的情形。
- 材料陈述的贡献
- 摘要称在相应设定下可将误差影响从标准差的一阶降至二阶，进一步修正可达三阶或更小，并指出一般识别障碍。
- 阅读关注点
- 应核对边界处的不连续性、误差分布条件、小误差渐近框架，以及未知误差分布时减偏与识别之间的区别。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化。摘要未完整给出误差阶改善的条件，减偏结论不能替代识别保证。
原文摘要
A range of problems in economics and statistics involve calculation of the boundary, or frontier, of the support of a distribution. Several practical and attractive solutions exist if the sampled distribution has a sharp discontinuity at the frontier, but accuracy can be greatly diminished if the data are observed with error. Indeed, if the error is additive and has variance σ2 then inaccuracies are usually of order σ, for small σ. In this article we suggest an elementary method for reducing the effect of error to O(σ2), and show that refinements can improve accuracy still further, to O(σ3) or less. The problem is inherently ill-posed, however, to such an extent that the frontier is generally not even identifiable unless the error distribution is known. The latter assumption is unreasonable in most practical settings, not in the least because the error is often asymmetrically distributed. For example, in the context of productivity analysis the error distribution tends to have a longer tail in the direction of underestimation of production. Nevertheless, even when the error distribution is unknown, it is often true that error variance is relatively low, and so methods for reducing systematic error in that case are useful in practice.