Sharp Local Minimax Rates for Goodness-of-Fit Testing in Large Random Graphs, multivariate Poisson families and multinomials

12/26/2020
by   J. Chhor, et al.
0

We consider the identity testing problem in large inhomogeneous random graphs (also called goodness-of-fit testing problem), multivariate Poisson families and multinomials. Given a known probability distribution P and n iid samples drawn from an unknown probability distribution Q, we investigate how large ρ should be to distinguish, with high probability, the case P=Q from the case d(P,Q) ≥ρ. We answer this question in the case of a family of distances: d(P,Q) = P-Q_t for t ∈ [1,2]. Besides being locally minimax-optimal (i.e. characterizing the detection threshold associated to the known matrix P), our tests have simple expressions and are easily implementable. Our results are closely related to important and popular results in the multinomial setting, and complete them by providing the missing matching upper and lower bounds.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/09/2021

Goodness-of-Fit Testing for Hölder-Continuous Densities: Sharp Local Minimax Rates

We consider the goodness-of fit testing problem for Hölder smooth densit...
research
11/15/2022

Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates

Given a heterogeneous Gaussian sequence model with unknown mean θ∈ℝ^d an...
research
02/01/2019

Local minimax rates for closeness testing of discrete distributions

We consider the closeness testing (or two-sample testing) problem in the...
research
06/30/2017

Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates

We consider the goodness-of-fit testing problem of distinguishing whethe...
research
12/03/2017

The local geometry of testing in ellipses: Tight control via localized Kolomogorov widths

We study the local geometry of testing a mean vector within a high-dimen...
research
12/03/2017

The local geometry of testing in ellipses: Tight control via localized Kolmogorov widths

We study the local geometry of testing a mean vector within a high-dimen...
research
07/12/2013

On Nicod's Condition, Rules of Induction and the Raven Paradox

Philosophers writing about the ravens paradox often note that Nicod's Co...

Please sign up or login with your details

Forgot password? Click here to reset