SEMINARS
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Fall 2007
STATISTICS
COLLOQUIUM
Monday, October 1, 2007
3:30-4:00—Refreshments
4:00-5:00—Talk
Yost Hall, Room 300
Richard Charnigo, PhD
Department of Statistics, University of Kentucky
Local and Global Analytic Curve Estimation
Many methods have been developed to estimate a mean response function, but most of these methods do not lend themselves to simultaneous estimation of the mean response and its derivatives. Being able to recover derivatives accurately is important for applications involving velocities and accelerations, for characterizing nanoparticles from scattering data, and for analyzing physical systems described by differential equations. We propose a ``compound estimator'' for an analytic mean response function. A novel feature of the compound estimator is that it combines information from multiple local estimators, each of which arises from a minimum distance problem expressed in a calculus of variations framework. The compound estimator is analytic and hence can be directly differentiated to estimate the derivatives of the mean response. We establish consistency results for both the local estimators and the compound estimator. In particular, the compound estimator and its derivatives converge uniformly to the mean response and (a finite but arbitrary number of) its derivatives on a compact interval. Issues of practical implementation are discussed, including a ``filtration and extrapolation'' refinement for finite samples. The empirical performance of the compound estimator is assessed with simulations and an application to real data.
This talk is based on joint work with Cidambi Srinivasan, University of Kentucky.
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