5 papers
Strong duality for the GROW criterion
Ashwin Ram, Martin Larsson, Johannes Ruf +1
This paper presents general strong duality results when testing hypotheses by betting against them. A bet is an e-variable for a composite null hypothesis $\Pcal$: a nonnegative ra…
A complete characterization of testable hypotheses
Martin Larsson, Johannes Ruf, Aaditya Ramdas
We revisit a fundamental question in hypothesis testing: given two sets of probability measures and , when does a nontrivial (i.e.\ strictly unbiased) te…
Testing hypotheses generated by constraints
Martin Larsson, Aaditya Ramdas, Johannes Ruf
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained…
Nonasymptotic and distribution-uniform Komlós-Major-Tusnády approximation
Ian Waudby-Smith, Martin Larsson, Aaditya Ramdas
We present nonasymptotic concentration inequalities for sums of independent and identically distributed random variables that yield asymptotic strong Gaussian approximations of Kom…
Distribution-uniform strong laws of large numbers
Ian Waudby-Smith, Martin Larsson, Aaditya Ramdas
We revisit the question of whether the strong law of large numbers (SLLN) holds uniformly in a rich family of distributions, culminating in a distribution-uniform generalization of…