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Activity Number: 591 - On Shape-Constrained Estimation and Inference
Type: Invited
Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #325517
Title: Isotonic Regression in general dimensions
Author(s): Sabyasachi Chatterjee*
Companies: University of Chicago

The estimation of a monotone signal in dimension d > 2 is a completely open problem. In this talk, I will present new results about the risk (in mean squared error) of the isotonic least squares (LSE) in general dimensions. Previously, results only existed for d = 1 and 2. In particular, I will talk about the minimax rate optimality (up to log factors) of the LSE in all dimensions and an automatic adaptation property which implies faster rates for special monotone signals. I will then compare our risk bounds for d > 2 with the d = 2 case arguing that there is a phase transition like phenomena as soon as d > 2 and highlight some surprising aspects of our results.

Authors who are presenting talks have a * after their name.

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