Robust Inference for Skewed data in Health Sciences

TL;DR

This paper introduces robust statistical methods for skew-normal distributions to improve inference accuracy in health data analysis, especially in the presence of outliers, through the minimum density power divergence approach.

Contribution

It develops a new class of robust estimators and tests for skew-normal distributions, including a symmetry test, with theoretical properties and practical algorithms.

Findings

Robust estimators outperform traditional methods in contaminated data.

The symmetry test remains effective despite outliers.

Applications demonstrate improved stability and accuracy in health data analysis.

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. 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.