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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 - #306302 |
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Title:
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Asymptotic Approximation to a Nonparametric Regression Experiment with Unknown Variance
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Author(s):
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Andrew Carter*+
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Companies:
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University of California, Santa Barbara
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Address:
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Department of Statistics, Santa Barbara, CA, 93106-3110,
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Keywords:
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nonparametric regression ; asymptotic equivalence of experiments
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Abstract:
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Brown and Low (1996) showed nonparametric regression experiments are asymptotically equivalent (in the sense of Le Cam's deficiency distance) to a Brownian motion process with an unknown drift function. Their result requires that the variance of the observations is known, but these variances generally are considered unknown nuisance parameters. Including the variance as an extra parameter in the definition of the regression experiment changes the form of the limiting experiment because a Brownian motion is completely informative about its variance. The appropriate approximation is a mixture of continuous Gaussian processes with different variances. The connection between the nonparametric regression and the mixed Gaussian process will be demonstrated for a homogeneous variance and a smooth variance function.
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