This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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320
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Type:
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Invited
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Date/Time:
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Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract - #306014 |
Title:
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P-Values for Classification in High-Dimensional Settings
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Author(s):
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Niki Zumbrunnen*+ and Lutz Dümbgen
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Companies:
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University of Bern and University of Bern
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Address:
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Alpeneggstrasse 22, Bern, International, 3012, Switzerland
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Keywords:
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nonparametric ;
regularization ;
data-driven tuning parameters ;
confidence region
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Abstract:
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Let (X,Y) be a random variable consisting of an observed feature vector X and an unobserved class label Y=1,2,...,L with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X,Y). Instead of providing point predictors (classifiers) for Y, we construct for each b=1,2,...,L a p-value pi_b(X,D) for the null hypothesis that Y=b, treating Y temporarily as a fixed parameter, i.e. we construct a prediction region for Y with a certain confidence. Any reasonable classifier can be modified to yield nonparametric p-values. For classifiers and p-values involving tuning parameters, we propose data-driven choices. One example are nearest neighbor classifiers. A second example is multicategory logistic regression , where we use regularization terms to deal with high-dimensional feature vectors X.
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