Consider k-independent normal populations with unknown means. Test the null hypothesis that the vector of means lies in a linear subspace (For example, the null could be all parameters are equal.) The alternative is that the vector of means lies in a closed convex cone (but not a linear subspace) whose dual cone is orthogonal to the linear subspace. Cohen et al. (2000, J. Multivariate Anal. 72, 50-77) showed that for many such cones the likelihood ratio test lacked a practical monotonicity property. Its behavior in such cases may be cause for concern. In this paper, we show that many Bayes tests also lack the practical monotonicity property.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Closed convex cone
- Complete class
- Cone order monotonicity
- Likelihood ratio test