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

  • Nobuhiro Taneichi
  • Yuri Sekiya
  • Hideyuki Imai


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 k 2 ) and the log-likelihood ratio statistic (G k 2 ) assuming sparseness. In this paper, we improve the asymptotic normality ofX k 2 andG k 2 statistics based on two kinds of normalizing transformation. The performance of the transformed statistics is numerically investigated.

Key words and phrases

Normalizing transformation PearsonX2 statistic log-likelihood ratio statistic sparse multinomials 


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Copyright information

© The Institute of Statistical Mathematics 2003

Authors and Affiliations

  • Nobuhiro Taneichi
    • 1
  • Yuri Sekiya
    • 2
  • Hideyuki Imai
    • 3
  1. 1.Obihiro University of Agriculture and Veterinary MedicineObihiroJapan
  2. 2.Hokkaido University of EducationKushiroJapan
  3. 3.Division of Systems and Information EngineeringHokkaido UniversitySapporoJapan

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