  In any parametric inference problem, the robustness of the procedure is a
real concern. A procedure which retains a high degree of efficiency under the
model and simultaneously provides stable inference under data contamination is
preferable in any practical situation over another procedure which achieves its
efficiency at the cost of robustness or vice versa. The density power
divergence family of Basu et al. (1998) provides a flexible class of
divergences where the adjustment between efficiency and robustness is
controlled by a single parameter $\beta$. In this paper we consider general
tests of parametric hypotheses based on the density power divergence. We
establish the asymptotic null distribution of the test statistic and explore
its asymptotic power function. Numerical results illustrate the performance of
the theory developed.
