TY - JOUR

T1 - Statistical testing under distributional shifts

AU - Thams, Nikolaj

AU - Saengkyongam, Sorawit

AU - Pfister, Niklas

AU - Peters, Jonas

PY - 2023

Y1 - 2023

N2 - We introduce statistical testing under distributional shifts. We are interested in the hypothesis for a target distribution ⁠, but observe data from a different distribution ⁠. We assume that is related to through a known shift τ and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and then applies an existing test in the target domain. We prove that if the size of the resample is of order and the resampling weights are well behaved, this procedure inherits the pointwise asymptotic level and power from the target test. If the map τ is estimated from data, we maintain the above guarantees under mild conditions on the estimation. Our results extend to finite sample level, uniform asymptotic level, a different resampling scheme, and statistical inference different from testing. Testing under distributional shifts allows us to tackle a diverse set of problems. We argue that it may prove useful in contextual bandit problems and covariate shift, show how it reduces conditional to unconditional indep

AB - We introduce statistical testing under distributional shifts. We are interested in the hypothesis for a target distribution ⁠, but observe data from a different distribution ⁠. We assume that is related to through a known shift τ and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and then applies an existing test in the target domain. We prove that if the size of the resample is of order and the resampling weights are well behaved, this procedure inherits the pointwise asymptotic level and power from the target test. If the map τ is estimated from data, we maintain the above guarantees under mild conditions on the estimation. Our results extend to finite sample level, uniform asymptotic level, a different resampling scheme, and statistical inference different from testing. Testing under distributional shifts allows us to tackle a diverse set of problems. We argue that it may prove useful in contextual bandit problems and covariate shift, show how it reduces conditional to unconditional indep

U2 - 10.1093/jrsssb/qkad018

DO - 10.1093/jrsssb/qkad018

M3 - Journal article

VL - 85

SP - 597

EP - 663

JO - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

SN - 1369-7412

IS - 3

ER -