Robust inference for skewed data in health sciences

ABSTRACT

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. 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.

Keywords:

• Skew normal (SN) distribution
• robust minimum density power divergence estimation
• wald-type test
• test for symmetry
• Genetic algorithm
• Influence function

Acknowledgements

The authors wish to thank the Editor and the two anonymous referees for their careful reading of the manuscript and several constructive suggestions which have significantly improved the paper. The research of the third author (AG) is partially supported by the INSPIRE Faculty Research Grant from Department of Science and Technology, Government of India, and the research of the first and third authors (AN and AG) are partially supported by a Start-up Research Grant from Indian Statistical Institute.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of the third author (A. G.) is partially supported by the INSPIRE Faculty Research Grant from Department of Science and Technology, Government of India, and the research of the first and third authors (A. N. and A. G.) are partially supported by a Start-up Research Grant from Indian Statistical Institute.