English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the identity testing problem - or goodness-of-fit testing problem- in multivariate binomial families, multivariate Poisson families andmultinomial distributions. Given a known distribution $p$ and $n$ iid samplesdrawn from an unknown distribution $q$, we investigate how large $\rho>0$should be to distinguish, with high probability, the case $p=q$ from the case$d(p,q) \geq \rho $, where $d$ denotes a specific distance over probabilitydistributions. We answer this question in the case of a family of differentdistances: $d(p,q) = \|p-q\|_t$ for $t \in [1,2]$ where $\|\cdot\|_t$ is theentrywise $\ell_t$ norm. Besides being locally minimax-optimal - i.e.characterizing the detection threshold in dependence of the known matrix $p$ -our tests have simple expressions and are easily implementable.

Sharp Local Minimax Rates for Goodness-of-Fit Testing in multivariate Binomial and Poisson families and in multinomials