🤖 AI Summary
This study addresses sample bias arising from unequal probability sampling or unobservable events by proposing a novel statistical test based on Rényi divergence, which is introduced here for the first time in the context of bias detection. The authors construct test statistics applicable to both uncensored and Type-I censored data, establishing favorable theoretical properties such as asymptotic normality. Critical values are determined via Monte Carlo simulations, and the method demonstrates robust performance across varying sample sizes and censoring proportions. Empirical analysis of two real-world datasets successfully identifies length bias, with the proposed test exhibiting higher power than existing approaches based on Kullback–Leibler divergence and likelihood ratios.
📝 Abstract
Weighted distributions arise in situations where observations are selected with unequal probabilities or because of the non-observability of some events. Detecting such sampling bias is essential for ensuring valid statistical inference. In this paper, we propose a statistical test for detecting bias in a sample using the Renyi divergence measure. The proposed test statistic is formulated for both uncensored and type-I censored data and possesses several theoretical properties including asymptotic normality. Critical values are obtained through simulations under the Weibull distribution for a range of sample sizes and censoring proportions. A comprehensive power study compares the proposed test with the existing Kullback-Leibler divergence-based test and the likelihood ratio test. Two real datasets are analyzed to demonstrate the practical utility of the proposed test in detecting length bias.