Econ Papers Daily / 期刊论文
高斯过程最大值点分布函数的连续性
Continuity of the Distribution Function of the argmax of a Gaussian Process
摘要
Certain extremum estimators have asymptotic distributions that are non‐Gaussian, yet characterizable as the distribution of the arg max of a Gaussian process. This paper presents high‐level sufficient conditions under which such asymptotic distributions admit a continuous distribution function. The plausibility of the sufficient conditions is demonstrated by verifying them in three examples, namely, maximum score estimation, empirical risk minimization, and threshold regression estimation. In turn, the continuity result buttresses several recently proposed inference procedures whose validity seems to require a result of the kind established herein. A notable feature of the high‐level assumptions is that one of them is designed to enable us to employ the Cameron–Martin theorem. In a leading special case, the assumption in question is demonstrably weak and appears to be close to minimal.
中文摘要
某些极值估计量的渐近分布并非高斯分布，但可表征为高斯过程最大值参数的分布。本文提出了高阶充分条件，在这些条件下，此类渐近分布具有连续分布函数。通过三个实例——最大得分估计、经验风险最小化和阈值回归估计——验证了这些充分条件的可行性。连续性结果进而支持了几种近期提出的推断方法，这些方法的有效性似乎依赖于本文所确立的这类结果。高阶假设的一个显著特点是，其中一项旨在使我们能够运用Cameron–Martin定理。在一个主要特例中，该假设被证明是弱的，且接近最小化。