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dc.contributor.authorSherwood, Ben
dc.contributor.authorWang, Lan
dc.identifier.citationSherwood, 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.
dc.description.abstractWe 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.en_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.rights© Institute of Mathematical Statistics, 2016en_US
dc.titlePartially linear additive quantile regression in ultra-high dimensionen_US
kusw.kuauthorSherwood, Ben
kusw.oanotesPer SHERPA/RoMEO 12/7/2017: Author's Pre-print: green tick author can archive pre-print (ie pre-refereeing) Author's Post-print: green tick author can archive post-print (ie final draft post-refereeing) Publisher's Version/PDF: green tick author can archive publisher's version/PDF General Conditions:

On author's personal website or open access repository On a non-profit server Version must be exactly as published in the journal Must link to publisher version PDF of all published articles are automatically placed in archiv Publisher's version/PDF may be used NIH authors may post authors' own version in PubMed Central for release 12 months after publication
kusw.oaversionScholarly/refereed, publisher versionen_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US

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