Multiple Decision Problem on Signs of Mean Vector in Three-Variate Normal Case

Abstract

Testing procedures can be considered decision procedures, and there exists the problem of how to deal with observed values of test statistics which fall in a neighborhood of the critical values. On the other hand, in the framework of the multiple decision problem, even if an incorrect decision is made, it may still be close to the correct decision, and may not exhibit the degree of error that would result from making decisions completely contrary to the truth. While testing procedures are conservative only in respect of rejection of the null hypothesis, multiple decision procedures are more conservative. In this paper we discuss the multiple decision problem on the signs of the components of the three-variate normal mean vector based on Takeuchi (1973), and study the behavior of multiple decision procedures by simulation.