  We consider a robust version of the classical Wald test statistics for
testing simple and composite null hypotheses for general parametric models.
These test statistics are based on the minimum density power divergence
estimators instead of the maximum likelihood estimators. An extensive study of
their robustness properties is given though the influence functions as well as
the chi-square inflation factors. It is theoretically established that the
level and power of these robust tests are stable against outliers, whereas the
classical Wald test breaks down. Some numerical examples confirm the validity
of the theoretical results.
