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SUMMARY:Two-sample testing of high-dimensional linear regression coefficie
 nts via complementary sketching - Tengyao Wang (LSE)
DTSTART:20220121T140000Z
DTEND:20220121T150000Z
UID:TALK168029@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:We introduce a new methodology for two-sample testing of high-
 dimensional linear regression coefficients without assuming that those coe
 fficients are individually estimable. The procedure works by first project
 ing the matrices of covariates and response vectors along directions that 
 are complementary in sign in a subset of the coordinates\, a process which
  we call 'complementary sketching'. The resulting projected covariates and
  responses are aggregated to form two test statistics. We show that our pr
 ocedure has essentially optimal asymptotic power under Gaussian designs wi
 th a general class of design covariance matrices when the difference betwe
 en the two regression coefficients is sparse and dense respectively. Simul
 ations confirm that our methods perform well in a broad class of settings.
LOCATION:MR12\, Centre for Mathematical Sciences
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