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Activity Number: 504
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #306034
Title: Uniform Convergence and Rate Adaptive Estimation of a Convex Function
Author(s): Xiao Wang*+ and Jinglai Shen
Companies: Purdue University and University of Maryland
Address: Department of Statistics, West Lafayette, IN, 47907-2066, USA
Keywords: adaptive nonprametric estimation ; Shape restricted estimation ; B-splines ; Holder class ; Minimax risk

This paper studies estimating a convex regression function in the univariate case. B-splines are used to approximate an underlying regression function. We show that the estimator is uniformly consistent with the optimal convergence rate. Asymptotically rate adaptive estimator of the convex regression function are proposed on the scale of Holder classes, with respect to pointwise and sup-norm risks.

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