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SUMMARY:Valid F-screening in linear regression - Daniela Witten (Universit
 y of Washington)
DTSTART:20251128T140000Z
DTEND:20251128T150000Z
UID:TALK237529@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Suppose that a data analyst wishes to report the results of a 
 least squares linear regression only if the overall null hypothesis—name
 ly\, that all non-intercept coefficients equal zero—is rejected. This pr
 actice\, which we refer to as F-screening (since the overall null hypothes
 is is typically tested using an F-statistic)\, is in fact common practice 
 across a number of applied fields. Unfortunately\, it poses a problem: sta
 ndard guarantees for the inferential outputs of linear regression\, such a
 s Type 1 error control of hypothesis tests and nominal coverage of confide
 nce intervals\, hold unconditionally\, but fail to hold conditional on rej
 ection of the overall null hypothesis. \n\nIn this talk\, I will present a
 n inferential toolbox for the coefficients in a least squares model that a
 re valid conditional on rejection of the overall null hypothesis. I will p
 resent selective p-values that lead to tests that control the selective Ty
 pe 1 error\, i.e.\, the Type 1 error conditional on having rejected the ov
 erall null hypothesis. Furthermore\, they can be computed without access t
 o the raw data\, using only the standard outputs of a least squares linear
  regression\, and therefore are suitable for use in a retrospective analys
 is of a published study. I will also present confidence intervals that att
 ain nominal selective coverage\, and point estimates that account for havi
 ng rejected the overall null hypothesis. \n\nI will illustrate this select
 ive procedure via re-analysis of a published result in the biomedical lite
 rature\, for which the raw data is not available. 
LOCATION:MR12\, Centre for Mathematical Sciences
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