An unbiased C-p type criterion for ANOVA model with a tree order restriction

作者：Inatsu Yu^*

来源：Hiroshima Mathematical Journal, 2017, 47(2): 181-216.

DOI：10.32917/hmj/1499392825

• Order restriction
• Tree ordering
• Model selection
• C-p
• UMVUE
• ANOVA

In this paper, we consider a C-p type criterion for ANOVA model with a tree ordering (TO) theta(1)<=theta(j) (j=2,...l) where theta(1),...,theta(1) are population means. In general, under ANOVA model with the TO, the usual C-p criterion has a bias to a risk function, and the bias depends on unknown parameters. In order to solve this problem, we calculate a value of the bias, and we derive its unbiased estimator. By using this estimator, we provide an unbiased C-p type criterion for ANOVA model with the TO, called TOCp. A penalty term of the TOCp is simply defined as a function of an indicator function and maximum likelihood estimators. Furthermore, we show that the TOCp is the uniformly minimum-variance unbiased estimator (UMVUE) of a risk function.

• 出版日期2017-7