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dc.contributor.authorSherwood, Ben
dc.contributor.authorWang, Lan
dc.date.accessioned2017-12-07T22:46:26Z
dc.date.available2017-12-07T22:46:26Z
dc.date.issued2016
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. https://projecteuclid.org/euclid.aos/1449755964en_US
dc.identifier.urihttp://hdl.handle.net/1808/25620
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
dc.typeArticleen_US
kusw.kuauthorSherwood, Ben
kusw.kudepartmentBusinessen_US
dc.identifier.doi10.1214/15-AOS1367en_US
kusw.oaversionScholarly/refereed, publisher versionen_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US
dc.rights.accessrightsopenAccessen_US


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