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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.

The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the presence of outliers in the data under such fully parametric proportional hazard models, a robust estimation procedure has recently been proposed extending the concept of the minimum density power divergence estimator (MDPDE) under this set-up. In this paper, we consider the problem of statistical inference under the parametric proportional hazards model and develop robust Wald-type hypothesis testing and model selection procedures using the MDPDEs. We have also derived the necessary asymptotic results which are used to construct the testing procedure for general composite hypothesis and study its asymptotic powers. The claimed robustness properties are studied theoretically via appropriate influence function analyses. We have studied the finite sample level and power of the proposed MDPDE based Wald-type test through extensive simulations where comparisons are also made with the existing semi-parametric methods. The important issue of the selection of appropriate robustness tuning parameter is also discussed. The practical usefulness of the proposed robust testing and model selection procedures is finally illustrated through three interesting real data examples.