How to detect a biased sample using the Renyi divergence measure?

Vaishnavi Pavithradas; Rajesh G

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arXiv · 2607.18790

How to detect a biased sample using the Renyi divergence measure?

Vaishnavi Pavithradas·Rajesh G

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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.

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Vaishnavi Pavithradas, Rajesh G. 2026-07-21. How to detect a biased sample using the Renyi divergence measure?. https://arxiv.org/abs/2607.18790

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