ODC and ROC curves, comparison curves, and stochastic dominance
Teresa Ledwina, Adam Zagda\'nski

TL;DR
This paper introduces comparison curves based on ordinal dominance and ROC, providing new visual and inferential tools for two-sample problems, improving detection of distributional differences with practical applications and simulations.
Contribution
It proposes novel comparison curves and B-plots for two-sample testing, enhancing interpretability and power over existing methods, with applications to stochastic dominance testing.
Findings
B-plots effectively summarize finite sample data.
Comparison tests outperform some classical tests in simulations.
Framework identifies regions with significant distributional differences.
Abstract
We discuss two novel approaches to the classical two-sample problem. Our starting point are properly standardized and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic curves, denoted by ODC and ROC, respectively. The proposed new curves are termed the comparison curves. Their estimates, being weighted rank processes on (0,1), form the basis of inference. These weighted processes are intuitive, well-suited for visual inspection of data at hand, and are also useful for constructing some formal inferential procedures. They can be applied to several variants of two-sample problem. Their use can help to improve some existing procedures both in terms of power and the ability to identify the sources of departures from the postulated model. To simplify interpretation of finite sample results we restrict attention to values of…
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Advanced Statistical Process Monitoring · Statistical Methods and Bayesian Inference
