  Health data are often not symmetric to be adequately modeled through the
usual normal distributions; most of them exhibit skewed patterns. They can
indeed be modeled better through the larger family of skew-normal distributions
covering both skewed and symmetric cases. However, the existing likelihood
based inference, that is routinely performed in these cases, is extremely
non-robust against data contamination/outliers. Since outliers are not uncommon
in complex real-life experimental datasets, a robust methodology automatically
taking care of the noises in the data would be of great practical value to
produce stable and more precise research insights leading to better policy
formulation. In this paper, we develop a class of robust estimators and testing
procedures for the family of skew-normal distributions using the minimum
density power divergence approach with application to health data. In
particular, a robust procedure for testing of symmetry is discussed in the
presence of outliers. Two efficient computational algorithms are discussed.
Besides deriving the asymptotic and robustness theory for the proposed methods,
their advantages and utilities are illustrated through simulations and a couple
of real-life applications for health data of athletes from Australian Institute
of Sports and AIDS clinical trial data.
