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Abstract Details
Activity Number:
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410
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract - #303342 |
Title:
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Shape-Restricted Penalized Splines
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Author(s):
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Xiao Wang*+
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Companies:
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Purdue University
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Address:
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, , ,
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Keywords:
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Green's Function ;
Complementarity Condition ;
Penalized Splines
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Abstract:
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Estimation of shape-restricted functions has broad applications in statistics, engineering, and science. In this talk, we first study the shape-restricted penalized spline regression estimators using constrained dynamical optimization techniques. The underlying regression function is approximated by a B-spline of an arbitrary degree subject to an arbitrary order difference penalty. The optimality conditions for spline coefficients give rise to a size-dependent complementarity problem. As a key technical result of the talk, the uniform Lipschitz property of optimal spline coefficients is established by exploiting piecewise linear and polyhedral theory. This property forms a cornerstone for stochastic boundedness, uniform convergence, and boundary consistency of the estimator. The estimator is then approximated by a solution of a differential equation subject to boundary conditions. This allows the estimator to be represented by a kernel regression estimator defined by a related Green's function of an ODE. The asymptotic normality is established at interior points via the Green's function.
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Authors who are presenting talks have a * after their name.
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