Testing Restricted Mean Vector Under Alternatives Hypothesis

Abstract

In most of the statistical models, the sign of the parameters are known is advance. In order to test the validity of the model, estimation and testing parameters to be done at the initial stage. In this case, usual unrestricted estimation and testing procedures may result in incorrect solutions. Usually, two-sided F or 2 χ testing are not suitable as well as unconstraint optimization solutions can give wrong estimate. In multivariate analysis, we usually apply two-sided Hotelling's -2 T for testing mean vector. This test may not be appropriate for testing when an order restriction is imposed among several p-variate normal mean vector. The main objective of this paper is for a given a multivariate normal population with unknown covariance matrix to develop a new testing procedure when the mean vector slipped to the right or to the left or both. So, we proposed a new distance based one sided and partially one sided Hotelling's -2 T to test restricted mean vectors. Monte Carlo simulations are conducted to compare power properties of the proposed 2 DT along with their respective conventional counterparts.