Improved Approximations for the Distributions of Multinomial Goodness-of-fit Statistics Based on φ-divergence under Nonlocal Alternatives
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- Htwe Pan Ei
- Department of System Information Science, Graduate School of Science and Engineering, Kagoshima University
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- Taneichi Nobuhiro
- Department of Mathematics and Computer Science, Graduate School of Science and Engineering (Science course), Kagoshima University
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- Sekiya Yuri
- Kushiro Campus, Hokkaido University of Education
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Abstract
Zografos et al. (1990) introduced the φ-divergence family of statistics Cφ to the goodness-of-fit test. The φ-divergence family of statistics Cφ includes the power divergence family of statistics proposed by Cressie and Read (Cressie and Read (1984) and Read and Cressie (1988)) as a special case. Sekiya and Taneichi (2004) derived the multivariate Edgeworth expansion assuming a continuous distribution for the distributions of power divergence statistics under a nonlocal alternative hypothesis. In this paper, we consider an expansion for the family of general φ-divergence statistics Cφ. We derive the multivariate Edgeworth expansion assuming a continuous distribution for the distribution of Cφ under a nonlocal alternative hypothesis. By using the expansion, we propose a new approximation for the power of the statistic Cφ. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we show that the present approximation is a good approximation especially when alternative hypotheses are distant from the null hypothesis.
Journal
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- JOURNAL OF THE JAPAN STATISTICAL SOCIETY
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JOURNAL OF THE JAPAN STATISTICAL SOCIETY 41 (2), 121-142, 2012
THE JAPAN STATISTICAL SOCIETY
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Details 詳細情報について
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- CRID
- 1390001205286970752
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- NII Article ID
- 10030497229
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- NII Book ID
- AA1105098X
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- ISSN
- 13486365
- 18822754
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- NDL BIB ID
- 023463461
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed