JSM 2011 Online Program

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Abstract Details

Activity Number: 410
Type: Contributed
Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #303342
Title: Shape-Restricted Penalized Splines
Author(s): Xiao Wang*+
Companies: Purdue University
Address: , , ,
Keywords: Green's Function ; Complementarity Condition ; Penalized Splines
Abstract:

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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