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Activity Number: 638
Type: Topic Contributed
Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #321005
Title: Estimation for Bivariate Quantile Varying Coefficient Model
Author(s): Linglong Kong* and Haoxu Shu and Chad He and Giseon Heo and Martin Styner and John Gilmore and Hongtu Zhu
Companies: University of Alberta and University of Alberta and Fred Hutchinson Cancer Research Center and University of Alberta and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
Keywords: bivariate quantile regression ; Propagation-Separation ; varying coefficient model ; Alternating Direction Method of Multipliers ; convex optimization ; Diffusion Tensor Imaging

We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$-type penalty is imposed to achieve desired smoothness. We develop a multistage estimation procedure based the Propagation-Separation~(PS) approach to borrow information from nearby directions. The PS method is capable of handling the computational complexity raised by simultaneously considering multiple directions to efficiently estimate varying coefficients while guaranteeing certain smoothness along directions. We reformulate the optimization problem and solve it by the Alternating Direction Method of Multipliers~(ADMM), which is implemented using R while the core is written in C to speed it up. Simulation studies are conducted to confirm the finite sample performance of our proposed method. A real data on Diffusion Tensor Imaging~(DTI) properties from a clinical study on neurodevelopment is analyzed.

Authors who are presenting talks have a * after their name.

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