Abstract Details
Activity Number:
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238
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Type:
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Contributed
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Date/Time:
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Monday, August 4, 2014 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #311121
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View Presentation
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Title:
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Likelihood Ratio Tests for Functional Linear Regression Models
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Author(s):
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Simeng Qu*+ and Xiao Wang
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Companies:
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Purdue University and Purdue University
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Keywords:
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generalized likelihood ratio test ;
functional linear model ;
optimal rate of convergence
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Abstract:
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This paper studies the global test of of nullity of the slope function in the framework of functional linear model and reproducing kernel Hilbert space. The quality of the test is measured by the minimal distance between the null and the alternative set for which such test is still possible. A generalized likelihood ratio test statistics is proposed and can be obtained by an easily implementable roughness-regularized estimator. The lower bound for the minimax separation distance of the slope function is derived. It is shown that the optimal rate is jointly determined by the reproducing kernel and the covariance kernel. However, this rate is different with the rate for prediction. It is shown that the generalized likelihood ratio test attains the optimal rate of convergence. Our simulations illustrate the promising performance of our approach and the method is further illustrated by an application of California air quality data.
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Authors who are presenting talks have a * after their name.
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