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Activity Number:
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254
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #305767 |
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Title:
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Local Analytic Curve Estimation
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Author(s):
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Richard Charnigo*+ and Cidambi Srinivasan
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Companies:
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University of Kentucky and University of Kentucky
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Address:
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851 Patterson Office Tower, Lexington, KY, 40506-0027,
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Keywords:
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nonparametric regression ; global modeling ; local modeling ; compound estimator ; calculus of variations
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Abstract:
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Consider a nonparametric regression problem in which the mean curve $\mu(x)$ is analytic. Seeking an analytic estimator with a tractable closed-form expression and without prior specification of an orthonormal basis, we formulate an integrated weighted least squares functional. Minimization of this functional reduces to solution of a second-order ordinary differential equation. The raw estimator is not consistent, but some modifications permit consistent estimation of Taylor approximants and the construction of a consistent ``compound estimator''. The compound estimator is analytic and can recover $\mu(x)$ at a uniform rate of nearly $n^{-1/2}$ on a compact set.
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