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Title	Adaptive confidence sets in shape restricted regression
Creator	Bellec, Pierre C
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-01-31T09:49
Description	We construct adaptive confidence sets in isotonic and convex regression. In univariate isotonic regression, if the true parameter is piecewise constant with $k$ pieces, then the Least-Squares estimator achieves a parametric rate of order $k/n$ up to logarithmic factors. We construct honest confidence sets that adapt to the unknown number of pieces of the true parameter. The proposed confidence set enjoys uniform coverage over all non-decreasing functions. Furthermore, the squared diameter of the confidence set is of order $k/n$ up to logarithmic factors, which is optimal in a minimax sense. In univariate convex regression, we construct a confidence set that enjoys uniform coverage and such that its diameter is of order $q/n$ up to logarithmic factors, where $q-1$ is the number of changes of slope of the true regression function. We will also discuss application of the presented techniques to sparse linear regression.
Extent	50 minutes
Subject	Mathematics Statistics Operations research, mathematical programming
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Rutgers
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-07-31
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0369258
URI	http://hdl.handle.net/2429/66625
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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