Lindsay Bruce G, Markatou Marianthi, Ray Surajit
Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802 (E-mail:
Professor at the Departments of Biostatistics and Biomedical Informatics, SUNY at Buffalo, 3435 Main Street, 726 Kimball Hall ; School of Public Health and Health Professions, and School of Medicine, Buffalo, NY 14260 (E-mail:
J Am Stat Assoc. 2014 Mar;109(505):395-410. doi: 10.1080/01621459.2013.836972. Epub 2014 Mar 19.
In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a , an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the , and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online.
在本文中，我们研究基于二次距离的拟合优度检验的功效性质。首先，我们引入一个概念并讨论在选择此核时所涉及的考虑因素。我们推导出一个易于使用的对二次距离拟合优度检验功效的正态近似，并在此基础上构建一个类似于传统非中心参数的。这导致了一种类似于奈曼 - 皮尔逊引理的方法，用于为特定备择假设构建最优核。然后，我们引入一个作为为感兴趣的一类备择假设选择最优自由度的工具。最后，我们引入一种新的扩散核，称为，并研究基于此核的检验功效的正态近似有效的程度。本文的补充材料可在线获取。
