AN ASYMPTOTIC APPROXIMATION FOR THE DISTRIBUTION OF ^|^phi;-DIVERGENCE MULTINOMIAL GOODNESS-OF-FIT STATISTIC UNDER LOCAL ALTERNATIVES
書誌事項
- タイトル別名
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- AN ASYMPTOTIC APPROXIMATION FOR THE DISTRIBUTION OF φ-DIVERGENCE MULTINOMIAL GOODNESS-OF-FIT STATISTIC UNDER LOCAL ALTERNATIVES
説明
On the goodness-of-fit test for multinomial distribution, Zografos et al.(1990)proposed the φ-divergence family of statistics, which includes the power divergence family of statistics as a special case. They showed that under null hypothesis, the members of the φ-divergence family of statistics all have an asymptotically equivalent chi-square distribution. Furthermore, Menendez et al.(1997)derived an asymptotic expansion for the null distribution of the φ-divergence statistic. In this paper, we derive an approximation for the distribution of the φ-divergence statistic under local alternatives. The approximation is based on the continuous term of the asymptotic expansion for the distribution of the φ-divergence statistic. By using the approximation, we propose a new approximation for the power of the statistic. The results are generalizations of those derived by Taneichi et al.which discussed the power divergence statistic. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we find that the present approximation performs better than the other approximations.
収録刊行物
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- ＪＯＵＲＮＡＬ ＯＦ ＴＨＥ ＪＡＰＡＮ ＳＴＡＴＩＳＴＩＣＡＬ ＳＯＣＩＥＴＹ
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ＪＯＵＲＮＡＬ ＯＦ ＴＨＥ ＪＡＰＡＮ ＳＴＡＴＩＳＴＩＣＡＬ ＳＯＣＩＥＴＹ 31 (2), 207-224, 2001
日本統計学会
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詳細情報 詳細情報について
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- CRID
- 1390282680262027008
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- NII論文ID
- 130003582736
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- ISSN
- 13486365
- 18822754
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可