Testing many restrictions under heteroskedasticity

Stanislav Anatolyev, Mikkel Sølvsten*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

Original languageEnglish
Article number105473
JournalJournal of Econometrics
Number of pages19
Publication statusPublished - Sept 2023


  • High-dimensional models
  • Hypothesis testing
  • Leave-out estimation
  • Linear regression
  • Many regressors
  • Ordinary least squares


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