Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Tests in adaptive regression via the Kac-Rice formula

Publication Date

August, 2013

Publication Type

Tech Report


Jonathan Taylor, Joshua Loftus, Ryan Tibshirani


We derive an exact p-value for testing a global null hypothesis in a general adaptive regression problem. The general approach uses the Kac-Rice formula, as described in (Adler & Taylor 2007). The resulting formula is exact in finite samples, requiring only Gaussianity of the errors. We apply the formula to the lasso, group lasso, and principal components and matrix completion problems. In the case of the lasso, the new test relates closely to the recently proposed covariance test of Lockhart et al. (2013).