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