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DTSTAMP:20250704T180159Z
DESCRIPTION:Title: The Inner Partial Least Square A Probe into the Necessar
 y” Dimension Reduction.\n\nAbstract: http://users.stat.umn.edu/~liux3771/
 \n\n\nThe partial least square (PLS) algorithm retains the combinations of
  predictors that maximize the covariance with the outcome. The Fisherian i
 nterpretation of PLS remained a mystery until Cook et al. (2013) showed th
 at it results in a predictor envelope\, which is the smallest reducing sub
 space of Σ X that contains the coefficient. This paper is motivated by fin
 dings after making a seemingly trivial change to the PLS: what if we chang
 e the max in PLS to min? Counterintuitively\, this does not calculate the 
 complement of the traditional PLS space. Instead\, it results in a new spa
 ce: the largest reducing subspace of Σ X that is contained in the coeffici
 ent matrix space. We define the modified PLS as the inner PLS and the resu
 lting space as the inner predictor envelope space. Unlike the traditional 
 PLS that removes irrelevant information\, the inner PLS incorporates the k
 nowledge that some information is purely relevant. Consequently\, the inne
 r PLS algorithm can lead to a more efficient regression estimator than the
  PLS in certain scenarios\; however\, it is not the most efficient under t
 he inner predictor envelope model. Therefore\, we derive the maximum likel
 ihood estimator and provide a non-Grassmannian optimization technique to c
 ompute it. We confirm the efficiency gain of our estimators both in simula
 tions and real-world data from the China Health and Nutrition survey.\n\n 
 \n\nVia Zoom - Please visit our website at: www.mcgill.ca/epi-biostat-occh
 /news-events/seminars/biostatistics \n
DTSTART:20220921T193000Z
DTEND:20220921T203000Z
SUMMARY:Lan Liu\, PhD\, University of Minnesota at Twin Cities
URL:/mathstat/channels/event/lan-liu-phd-university-mi
 nnesota-twin-cities-342052
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