The Projected Covariance Measure for assumption-lean variable significance testing. (arXiv:2211.02039v1 [math.ST])

Testing the significance of a variable or group of variables $X$ for
predicting a response $Y$, given additional covariates $Z$, is a ubiquitous
task in statistics. A simple but common approach is to specify a linear model,
and then test whether the regression coefficient for $X$ is non-zero. However,
when the model is misspecified, the test may have poor power, for example when
$X$ is involved in complex interactions, or lead to many false rejections. In
this work we study …

arxiv covariance lean math significance testing