The admissibility of the LRT for the exponential family model

In this paper we derive the LRT for testing a simple hypothesis about the natural parameter of a multivariate exponential family versus two sided alternatives. Moreover, we utilize the results of [Ann. Math. Stat. 27 (1956) 616, 41 (1970) 1884] to show that the LRT is admissible in the sense of Wald.