|
Abstract:
|
Consider a probability model with T-parameters(?¹,?²,...,?_{k}). The problem of testing null hypothesis H0:?¹=?²=...=?_{k} against selecting one of k-alternative hypotheses H_{i}:?_{i}=?_{[k]}, i=1,2,...,k, where ?_{[k]}=max{?¹,?²,...,?_{k}}, is formulated from a Bayesian decision theoretic point of view. This problem can be viewed as selecting a component with the largest parameter value if the null hypothesis is rejected. Some interesting loss functions are considered, and Bayes rules are obtained for the k-normal populations under these loss functions. It is demonstrated through this example that the classical hypothesis testing yields unnecessarily large acceptance region and thus unnecessarily fails to reject H0 when the purpose is to find the component with the largest parameter value. Consequences of this for the high dimensional data such as microarray data is pointed out.
|
