Robust Jarque–Bera-Type Tests for Normality: Improved Power and Error Control in Small and Non-normal Samples

Accepted January 2026

Abstract

This paper introduces two theoretically grounded robust adaptations of the Jarque–Bera (JB) test, denoted JB∗ and JB∗∗, designed to address key limitations of classical normality tests in the presence of outliers and non-normal data. The JB∗ test systematically replaces conventional moment based skewness and kurtosis with robust alternatives — Pearson median skewness and MAD-based kurtosis — motivated by breakdown-point theory and influence function analysis. The scaling constants are justified through asymptotic theory and empirical calibration. The JB∗∗ test employs variance-stabilizing nonlinear transformations of classical moments, with parameters optimized through a principled framework balancing Type I error control, average power, and stability across alternatives. (...) Applications to mechanical strain and COVID-19 data illustrate practical utility. Our work advances normality testing methodology by providing theoretically justified, reproducible alternatives with clear performance characteristics and practical guidance for test selection.