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SUMMARY:Residual Permutation Test for High-Dimensional Regression Coeffici
 ent Testing - Yuhao Wang\, Tsinghua University
DTSTART:20230908T130000Z
DTEND:20230908T140000Z
UID:TALK205045@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:We consider the problem of testing whether a single coefficien
 t is equal to zero in fixed-design linear models with moderately high-dime
 nsional covariates. In the moderate high-dimensional setting where the dim
 ension of covariates p is allowed to be in the same order of magnitude as 
 sample size n\, to achieve finite-population validity\, existing methods u
 sually require strong distributional assumptions on the noise vector (such
  as Gaussian or rotationally invariant)\, which limits their applications 
 in practice. In this paper\, we propose a new method\, called residual per
 mutation test (RPT)\, which is constructed by projecting the regression re
 siduals onto the space orthogonal to the union of the column spaces of the
  original and permuted design matrices. RPT can be proved to achieve finit
 e-population size validity under fixed design with just exchangeable noise
 s\, whenever p < n / 2. Moreover\, RPT is shown to be asymptotically power
 ful for heavy tailed noises with bounded (1+t)-th order moment when the tr
 ue coefficient is at least of order n^{-t / (1 + t)} for t \\in [0\, 1]. W
 e further proved that this signal size requirement is essentially minimax 
 rate optimal. Numerical studies confirm that RPT performs well in a wide r
 ange of simulation settings with normal and heavy-tailed noise distributio
 ns. This is based on joint works with Kaiyue Wen and Tengyao Wang.
LOCATION:MR12\, Centre for Mathematical Sciences
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