Research map / Learning theory and algorithms / Sample complexity
Multivariate tests of association based on univariate tests
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply a consistent univariate test to distances from a single center point (distance-based reduction) instead of testing the multivariate distribution directly | multivariate two-sample / independence testing · theoretical (Corollary, almost every center point) | power as sample size grows | Helped |
| Aggregate univariate tests over multiple center points (max/sum of KS statistics, or combined p-values) rather than a single center | two-sample KS-based multivariate test · theoretical (Theorem on pooled KS tests) | consistency / power to one | No clear effect |
| Use the sample points themselves as center points with a U-statistic univariate test averaged across centers | univariate U-statistic of order m · theoretical | order of resulting U-statistic | No clear effect |
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