Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

✍ Scribed by Nobuhiro Taneichi; Yuri Sekiya; Akio Suzukawa

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 172 KB
• Volume: 81
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2001.2002

✦ Synopsis

introduced a class of multinomial goodness-of-fit statistics R a based on power divergence. All R a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R a under local alternatives. We obtain an expression of approximation for the distribution of R a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R a . We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R a . We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.