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Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests

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  • Bruce G. Lindsay
  • Marianthi Markatou
  • Surajit Ray

Abstract

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.

Suggested Citation

  • Bruce G. Lindsay & Marianthi Markatou & Surajit Ray, 2014. "Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 395-410, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:395-410
    DOI: 10.1080/01621459.2013.836972
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    Cited by:

    1. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    2. Pavia, Jose M., 2015. "Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(c01).
    3. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    4. Norbert Henze & Pierre Lafaye De Micheaux & Simos G. Meintanis, 2022. "Tests for circular symmetry of complex-valued random vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 488-518, June.

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