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Activity Number:
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118
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Type:
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Invited
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Date/Time:
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Monday, July 30, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #307701 |
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Title:
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Penalized Splines: Asymptotics with Increasing Number of Knots and Equivalent Kernels
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Author(s):
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David Ruppert*+ and Yingxing Li
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Companies:
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Cornell University and Cornell University
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Address:
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School of OR & IE 225 Rhodes Hall, Ithaca, NY, 14853 ,
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Keywords:
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equivalent kernel ; binning
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Abstract:
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The asymptotic behavior of univariate B-splines estimated with a difference penalty is studied. Penalized splines behave like kernel estimators with "equivalent" kernels depending upon the order of the penalty. The number of knots is assumed to converge to infinity. The asymptotic distribution of the penalized spline estimate is Gaussian with simple expressions for the asymptotic mean and variance. Providing that it is fast enough, the rate at which the number of knots converges to infinity does not affect the asymptotic distribution. The optimal rate of convergence of the penalty parameter is given. Penalized splines are not in general design-adaptive. Bias decomposes into modeling and smoothing bias due to spline approximation and penalization, respectively. In our framework, the first is asymptotically negligible and the second is controlled by the penalty parameter.
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