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Abstract Details
Activity Number:
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5
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Type:
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Invited
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Date/Time:
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Sunday, July 29, 2012 : 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 - #303637 |
Title:
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Nonparametric and Semiparametric Quantile Regression via Global MM Algorithms
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Author(s):
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Bo Kai*+ and Mian Huang and Weixin Yao
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Companies:
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College of Charleston and Shanghai University of Finance and Economics and Kansas State University
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Address:
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Department of Mathematics, Charleston, SC, 29424,
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Keywords:
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Quantile Regression ;
MM Algorithms ;
Nonparametric Regression
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Abstract:
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Nonparametric and semiparametric quantile regression models are widely used statistical models in many research fields and applications. The modeling procedures often relate to the optimization of a set of locally weighted quantile functions. However, the optimization is very challenging because the objective functions are non-differentiable and the estimation procedures are often complex. In this work, we propose a class of new MM algorithms, termed the global MM algorithms, for a variety of nonparametric and semiparametric quantile regression models. By introducing a global residual, the proposed algorithms simultaneously minimize a set of locally weighted quantile loss functions, and yield continuous and smooth estimates. We systematically study the global MM algorithm in the local linear quantile regression setting, and show that the proposed algorithm preserves the descent property of MM algorithms in an asymptotic sense. We further study the applications of the global MM algorithms for several popular nonparametric and semiparametric quantile regression models. The finite sample performance of the proposed algorithms is examined via extensive Monte Carlo simulation studies.
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