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    Partially linear additive quantile regression in ultra-high dimension

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    Sherwood_2016.pdf (320.9Kb)
    Issue Date
    2016
    Author
    Sherwood, Ben
    Wang, Lan
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    © Institute of Mathematical Statistics, 2016
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    Abstract
    We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates nonlinearity and circumvents the curse of dimensionality. (4) It is naturally robust to heavy-tailed distributions. In this paper, we approximate the nonlinear components using B-spline basis functions. We first study estimation under this model when the nonzero components are known in advance and the number of covariates in the linear part diverges. We then investigate a nonconvex penalized estimator for simultaneous variable selection and estimation. We derive its oracle property for a general class of nonconvex penalty functions in the presence of ultra-high dimensional covariates under relaxed conditions. To tackle the challenges of nonsmooth loss function, nonconvex penalty function and the presence of nonlinear components, we combine a recently developed convex-differencing method with modern empirical process techniques. Monte Carlo simulations and an application to a microarray study demonstrate the effectiveness of the proposed method. We also discuss how the method for a single quantile of interest can be extended to simultaneous variable selection and estimation at multiple quantiles.
    URI
    http://hdl.handle.net/1808/25620
    DOI
    https://doi.org/10.1214/15-AOS1367
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    • School of Business Scholarly Works [213]
    Citation
    Sherwood, Ben; Wang, Lan. Partially linear additive quantile regression in ultra-high dimension. Ann. Statist. 44 (2016), no. 1, 288--317. doi:10.1214/15-AOS1367. https://projecteuclid.org/euclid.aos/1449755964

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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