We study the problem of testing the hypothesis that the mean vector of a random vector belongs to a given set. For this purpose, we consider a semiparametric mixture of DIRICHLET PROCESS model in which the mean vector has a prior distribution concentrated on the set of interest. A computational method is given to obtain a sample from the posterior distribution of the mean vector. On the basis of this sample, we can obtain the Bayes estimate and the posterior probability that the hypothesis is true. We give a numerical example to demonstrate the application of this method.

Let Bn be the open unit ball in C n and B 2 n = Bn×Bn. The symmetric lifting operator which lifts analytic functions from H(Bn) to H(B 2 n ) is defined as follow L(f)(z, w) = f(z)-f(w)/z-w In this paper we investigate the action of symmetric lifting operator on the Bergman space in the unit ball. Also, we state a characterization for DIRICHLET space and consider symmetric lifting operator on the DIRICHLET space in the unit ball.