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Marginal Coordinate Test for Fr\'echet Regression with Random Objects
AI InsightThis paper introduces a marginal coordinate test for random-object regression in separable metric spaces, using a semi-supervised framework and a kernel conditional mean dependence U-statistic to test predictor informativeness without response residuals. Compared with prior residual-based tests, it relaxes assumptions and broadens applicability.Key TakeawayUnlike previous residual-based tests, this method avoids response residuals and works in general metric spaces.Why It MattersIt provides a more general hypothesis-testing tool for regression with complex structured responses, advancing statistical modeling on non-Euclidean data.Who's Affected- AI ResearchersGain a new theoretical tool to test conditional effects of predictors in random-object regression, extending statistical inference limits.
What's NextWatch for empirical performance on large semi-supervised datasets and theoretical adaptations to non-separable metric spaces or nonlinear relationships.Importance 70/100