Sharp local minimax rates for goodness-of-fit testing in multivariate binomial and Poisson families and in multinomials
Julien ChhorCREST-ENSAE, Palaiseau, France
Alexandra CarpentierUniversität Potsdam, Germany
We consider the identity testing problem – or goodness-of-fit testing problem – in multivariate binomial families, multivariate Poisson families and multinomial distributions. Given a known distribution and i.i.d. samples drawn from an unknown distribution , we investigate how large should be to distinguish, with high probability, the case from the case , where denotes a specific distance over probability distributions. We answer this question in the case of a family of different distances: for , where is the entrywise norm. Besides being locally minimax-optimal – i.e. characterizing the detection threshold in dependence of the known matrix – our tests have simple expressions and are easily implementable.
Cite this article
Julien Chhor, Alexandra Carpentier, Sharp local minimax rates for goodness-of-fit testing in multivariate binomial and Poisson families and in multinomials. Math. Stat. Learn. 5 (2022), no. 1/2, pp. 1–54DOI 10.4171/MSL/32