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Comparative Frameworks for Relative Multivariate Analysis

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In this paper, I develop new methods for comparative analysis of multivariate data, such as multiple financial asset returns, paired biomedical data, performance metrics across cross-validation folds or test sets for various machine learning algorithms or hyperparameter choices, user ratings of various products, voter ratings of political candidates and their policy proposals, or experimental data arranged in complete block designs. My approaches involve transforming the original data into bounded relative measures and are grounded in axiomatic frameworks, which are inspired by the Ricardian notion of comparative advantage. The resulting statistical procedures serve as general alternatives to some widely used nonparametric tests, such as the sign test and the Friedman test. My methodologies have applications in several areas. For example, they are useful for conducting portfolio analysis and technical analysis in finance from a relative perspective. Users of online marketplaces or streaming services or review platforms may find relative ratings of products and services helpful. The general frameworks are also useful for building machine learning algorithms or statistical models that minimize loss functions based on interpretable relative prediction errors. In addition, some of the proposed relative measures can themselves be practically treated as outcomes for causal analysis in some settings.

This talk is part of the Causal Inference Reading Group series.

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