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Improvements of goodness-of-fit statistics for sparse multinomials based on normalizing transformations

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Abstract

We consider multinomial goodness-of-fit tests for a specified simple hypothesis under the assumption of sparseness. It is shown that the asymptotic normality of the PearsonX 2 statistic (X 2 k ) and the log-likelihood ratio statistic (G 2 k ) assuming sparseness. In this paper, we improve the asymptotic normality ofX 2k andG 2 k statistics based on two kinds of normalizing transformation. The performance of the transformed statistics is numerically investigated.

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Authors and Affiliations

  1. Obihiro University of Agriculture and Veterinary Medicine, Inada-cho, 080-8555, Obihiro, Japan

    Nobuhiro Taneichi

  2. Hokkaido University of Education, Kushiro Campus, Shiroyama, 085-8580, Kushiro, Japan

    Yuri Sekiya

  3. Division of Systems and Information Engineering, Hokkaido University, 060-8628, Sapporo, Japan

    Hideyuki Imai

Authors
  1. Nobuhiro Taneichi
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  2. Yuri Sekiya
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  3. Hideyuki Imai
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Taneichi, N., Sekiya, Y. & Imai, H. Improvements of goodness-of-fit statistics for sparse multinomials based on normalizing transformations. Ann Inst Stat Math 55, 831–848 (2003). https://doi.org/10.1007/BF02523396

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  • DOI: https://doi.org/10.1007/BF02523396

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