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