Kernels, degrees of freedom, and power properties of quadratic distance goodness-of-fit tests

• Autores: Bruce G. Lindsay, Marianthi Markatou, Surajit Ray
• Localización: Journal of the American Statistical Association, ISSN 0162-1459, Vol. 109, Nº 505, 2014, págs. 395-410
• Idioma: inglés
• DOI: 10.1080/01621459.2013.836972
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• Resumen

  • 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.