COLLOQUIUM "When Pearson $\chi^2$ and other divisible statistics are not goodness-of-fit tests" by Sara Algeri (University of Minnesota)

Friday 24 May 2024, 11:00 → 12:00 Europe/Amsterdam

This talk introduces a unifying approach to the analysis of binned data which allows us to study the class of divisible statistics  --  that includes Pearson's $\chi^2$, the likelihood ratio as special cases  --  from a new perspective.

Such a study reveals that no single divisible statistic is adequate for goodness-of-fit.
It also shows that, in a sparse regime, all tests proposed in the literature are dominated by a class of weighted linear statistics.
The construction of goodness-of-fit distribution-free tests is also discussed.