The role of higher-order moments in assessing estimator’s normality under scrambled response modeling

Normality is a basic requirement in most of the statistical methods and provides the foundation for valid statistical inference. Skewness and kurtosis (defined in terms second, third, and fourth mean moments), which are measures of asymmetry and tail shape, are important measures of whether normality can be assumed for a given set of data. Knowledge of these higher-order moments is significant for determining the stability and robustness of estimators. The role of these in determining distributional characteristics is examined in this study, with specific emphasis on scrambled response models. With both the theoretical and simulation studies, we examine performance of scrambled response estimators under normality hypotheses by using well known Jarque–Bera statistic. The findings emphasize the role of higher-order moments in evaluating estimator’s robustness and illuminate their behavior in applications.