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SUMMARY:Recent Developments in the Study of Single-Index Type Models - Mou
 li Banerjee\, University of Michigan
DTSTART:20190607T130000Z
DTEND:20190607T140000Z
UID:TALK119416@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Single-index type models are popular in statistics\, biostatis
 tics and economics as they alleviate the curse of dimensionality to a cons
 iderable extent while allowing for broad classes of models through the dep
 endence on an unknown link function. Various classes of single index model
 s are known: in regular models under a fixed dimension setting [i.e. fixed
  number of regression parameters]\, the regression parameter is √n estim
 able\; under current status type censoring of the response variable in a l
 inear regression model — which leads to the binary choice model — one 
 gets a generalized single-index model where the rate of estimation is at m
 ost n^{1/3}\, a problem well-studied in the econometrics literature (by Ma
 nski and subsequent authors). Single index structures with a discontinuous
  link function arise in models involving change-planes in multidimensional
  space — hyperplanes that separate two (or more) response or survival re
 gimes — and are relevant to applications in personalized medicine and dy
 namic treatment regimes. Here\, rates of estimation can easily exceed √n
  in the finite dimensional case.  \n\nI will talk about some of my recent 
 work in the above class of models in growing and high dimensional settings
  focusing on how growing dimensions introduce significantly new challenges
  at both theoretical and computational levels and present some recent resu
 lts on convergence\, minimax-optimal rates\, and inference\, as well as fu
 ture challenges.  \n\nThe talk is based on joint work with Ya'acov Ritov\,
  Hamid Eftekhari\, Zhiyuan Lu and Debarghya Mukherjee.
LOCATION:MR12
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