Properties of Correlation Determination Based on Qn Estimator for Standard Logistic Distribution with Contamination

Robust statistical methods have become increasingly important in the presence of contaminated data, particularly in regression-based goodness of fit testing. The classical coefficient of determination is highly sensitive to deviations from assumptions such as normality and the absence of contaminated data. To address this limitation, this study investigates the properties of a robust coefficient of determination derived from the Qn estimator, which is a high-breakdown-point scale estimator. This research focuses on the behaviour of the sampling distribution under the standard logistic distribution with varying contamination structures. A comprehensive simulation study is conducted under different sample sizes, contamination levels and distributions of the contaminants. Bootstrap bias-corrected and accelerated (BCa) confidence intervals are constructed to evaluate the estimator’s statistical properties in the presence of contaminated data. Results demonstrate that contamination significantly influences skewness and variability, although the estimator remains bounded and robust.