  Randomly censored survival data are frequently encountered in applied
sciences including biomedical or reliability applications and clinical trial
analyses. Testing the significance of statistical hypotheses is crucial in such
analyses to get conclusive inference but the existing likelihood based tests,
under a fully parametric model, are extremely non-robust against outliers in
the data. Although, there exists a few robust parameter estimators (e.g.,
M-estimators and minimum density power divergence estimators) given randomly
censored data, there is hardly any robust testing procedure available in the
literature in this context. One of the major difficulties in this context is
the construction of a suitable consistent estimator of the asymptotic variance
of M estimators; the latter is a function of the unknown censoring
distribution. In this paper, we take the first step in this direction by
proposing a consistent estimator of asymptotic variance of the M-estimators
based on randomly censored data without any assumption on the form of the
censoring scheme. We then describe and study a class of robust Wald-type tests
for parametric statistical hypothesis, both simple as well as composite, under
such set-up, along with their general asymptotic and robustness properties.
Robust tests for comparing two independent randomly censored samples and robust
tests against one sided alternatives are also discussed. Their advantages and
usefulness are demonstrated for the tests based on the minimum density power
divergence estimators with specific attention to clinical trial analyses.
