标题： 概率的二次距离：一个统一的基础 显示英文标题

标题： Quadratic distances on probabilities: A unified foundation

摘要： 本文构建了一个统一的框架，用于研究作为评估模型拟合优度所使用的二次型距离度量。许多重要的程序都具有这种结构，但这些方法的理论分散且不完整。这些距离统计分析的核心在于生成距离的核函数的谱分解。我们展示了这如何决定了自然拟合优度检验的极限分布。此外，我们基于此分解发展了一种新的概念，即检验的谱自由度。自由度易于计算和估计，并可作为构建此类中有用程序的指南。 显示英文摘要

摘要： This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness-of-fit tests. Additionally, we develop a new notion, the spectral degrees of freedom of the test, based on this decomposition. The degrees of freedom are easy to compute and estimate, and can be used as a guide in the construction of useful procedures in this class.