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Activity Number:
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291
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 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 - #305744 |
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Title:
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Shape-Restricted Spline Regression
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Author(s):
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Xiao Wang*+
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Companies:
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University of Maryland Baltimore County
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Address:
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Department of Math and Statistics, Baltimore, MD, 21250,
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Keywords:
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isotonic regression ; second order cone programming ; reversible jump MCMC
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Abstract:
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The isotonic smoothing spline regression problem is considered. Such estimator is characterized as a nondecreasing natural cubic spline. We give a necessary and sufficient condition for a cubic function nondecreasing over an interval. Estimation of the unknown parameters is formulated into a second-order cone programming problem. The resulting estimated regression function is preserved nondecreasing in the whole domain and also has enough smoothness. Simulation results suggests the method performs well and we illustrate the method by ASA car data. If time permits, we also propose a new Bayesian approach for monotone curve estimation. We treat the number and locations of knots as free parameters and use reversible jump Markov chain Monte Carlo to obtain the posterior samples of knot configurations.
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