Distribution-Free Simultaneous Confidence Intervals Based on Wilcoxon's Rank Statistics in the One-Way Layout

• Shiraishi Taka-aki

Bibliographic Information

Other Title

• 多群モデルにおけるウィルコクソンの順位和に基づくノンパラメトリック同時信頼区間
• タグン モデル ニ オケル ウィルコクソン ノ ジュンイワ ニ モトズク ノンパラメトリック ドウジ シンライ クカン

Abstract

We consider simultaneous confidence intervals based on rank statistics of Wilcoxon-type in one-way layout. Using exact simultaneous rank tests and using Gauss's notation, we give exact expressions for the procedures of the simultaneous confidence intervals. Furthermore, we give two expressions of the asymptotic simultaneous confidence intervals. Although the distributions for the normal theory pocedures are given by double integrals, the asymptotic distributions for the proposed procedures are expressed as single integrals. Especially, we derive the upper and lower bounds for the asymptotic distribution of Tukey-type statistics. From simulation, we can see that the asymptotic simultaneous confidence intervals are conservative. When sample sizes are large, we recommend the simultaneous confidence intervals based on the Monte Carlo simulation. When the sizes of all samples are large, it is found that the rank procedures are superior to the classical normal theory procedures except the case that an underlying distribution is nearly normal.

Journal

• Ouyou toukeigaku

  Ouyou toukeigaku 37 (3), 125-150, 2008

  Japanese Society of Applied Statistics

Keywords

• single-step procedures
• exact probability
• asymptotics
• efficiency
• simulation

Details

• CRID: 1390282679419058944
• NII Article ID: 130002136761
• NII Article ID: 10024748999
• NII Book ID: AN00330942
• DOI: 10.5023/jappstat.37.125
• ISSN: 18838081
• ISSN: 02850370
• NDL BIB ID: 9803544
• Web Site: http://id.ndl.go.jp/bib/9803544
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9803544
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed