Discrete Bartlett-Type Transformed Statistics Using a Discontinuous Term of Asymptotic Expansion

• Sekiya Yuri

  北海道教育大学教育学部釧路校

• Taneichi Nobuhiro

  鹿児島大学理工学研究科

Bibliographic Information

Other Title

• 漸近展開の不連続項を利用した離散バートレット型変換統計量
• ゼンキン テンカイ ノ フレンゾクコウ オ リヨウ シタ リサン バートレットガタ ヘンカン トウケイリョウ

Abstract

In the multinomial goodness-of-fit test, it is well known that the log-likelihood ratio statistic T has a limiting chi-square distribution under a simple null hypothesis. Siotani and Fujikoshi (1984) derived an asymptotic expansion for the null distribution of the log-likelihood ratio statistic T under a simple null hypothesis. They proposed J₁+Ĵ₂ as an approximation of the lower probability of T, where J₁ is a term of multivariate Edgeworth expansion and Ĵ₂ is a first order approximation of a discontinuous term. In this paper, we introduce discrete Bartlett-type transformed statistics T^* and T^** of the log-likelihood ratio statistic T that are constructed from J₁ and Ĵ₂. By numerical comparison, we found that the accuracy of approximation of the log-likelihood ratio statistic T to a chi-square distribution is improved by T^* or T^**.

Journal

• Journal of the Japan Statistical Society, Japanese Issue

  Journal of the Japan Statistical Society, Japanese Issue 45 (1), 1-17, 2015

  Japan Statistical Society

Keywords

• 多項分布の適合度検定
• 対数尤度比統計量
• 離散バートレット型変換
• 漸近展開の不連続項

Details

• CRID: 1390282679415073408
• NII Article ID: 130005153218
• NII Book ID: AA1105098X
• DOI: 10.11329/jjssj.45.1
• ISSN: 21891478
• ISSN: 03895602
• NDL BIB ID: 026806549
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I026806549
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed