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SUMMARY:Reduced Isotonic Regression - Chao Gao (University of Chicago)
DTSTART:20180626T084500Z
DTEND:20180626T093000Z
UID:TALK107395@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Consider an $n$-dimensional vector $X$ with mean $\\theta^*$. 
 In this talk\, we consider $\\theta^*$ that is both nondecreasing and has 
 a piecewise constant structure. We establish the exact minimax rate of est
 imating such monotone functions\, and thus give a non-trivial answer to an
  open problem in the shape-constrained analysis literature. The minimax ra
 te involves an interesting iterated logarithmic dependence on the dimensio
 n. We then develop a penalized least-squares procedure for estimating $\\t
 heta^*$ adaptively. This estimator is shown to achieve the derived minimax
  rate without the knowledge of the number of pieces in linear time. We fur
 ther allow the model to be misspecified and derive oracle inequalities wit
 h the optimal rates for the proposed estimator. This is a joint work with 
 Fang Han and Cun-hui Zhang.
LOCATION:Seminar Room 1\, Newton Institute
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