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Inference on the overlap coefficient: The binormal approach and alternatives.

Alba María Franco-Pereira^1,2, Christos T Nakas^3,4, Benjamin Reiser⁵

¹Department of Statistics and OR, Complutense University of Madrid, Spain.

Statistical Methods in Medical Research

|October 25, 2021

Summary

This study introduces new methods for calculating the overlap coefficient, a measure of distribution similarity. Parametric approaches, particularly the binormal model, offer superior performance for applied researchers.

Keywords:

Bootstrap Box-Cox transformation ROC curve analysis delta method kernel methods

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Area of Science:

Statistics
Biostatistics

Background:

The overlap coefficient quantifies similarity between two distributions.
Accurate confidence interval methods are needed for applied researchers.
Existing methods lack software and broad applicability.

Purpose of the Study:

Develop accurate parametric and non-parametric methods for overlap coefficient confidence intervals.
Provide R-code for implementation.
Address limitations in current literature.

Main Methods:

Developed parametric and non-parametric inferential procedures.
Utilized the binormal model for parametric approaches.
Assessed methods via a large simulation study.

Main Results:

Parametric methods, especially the binormal model, demonstrated superior performance.
The developed methods are suitable for diverse distributional scenarios.
R-code facilitates practical implementation.

Conclusions:

The study provides robust statistical methods for the overlap coefficient.
Parametric approaches offer reliable confidence intervals for distribution similarity.
Findings are applicable to fields like cognitive function assessment.