Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests
成果类型：
Article
署名作者：
Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit
署名单位：
Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; State University of New York (SUNY) System; University at Buffalo, SUNY; State University of New York (SUNY) System; University at Buffalo, SUNY; State University of New York (SUNY) System; University at Buffalo, SUNY; University of Glasgow
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2013.836972
发表日期：
2014
页码：
395-410
关键词：
摘要：
In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel 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 noncentrality index, 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 midpower analysis 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 Pearson-normal kernel, 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.