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作者：Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia
作者单位：Harvard University; University of South Carolina System; University of South Carolina Columbia; Columbia University
摘要：We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The ...
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作者：Hoffmann, Marc; Rousseau, Judith; Schmidt-Hieber, Johannes
作者单位：Universite PSL; Universite Paris-Dauphine; Leiden University - Excl LUMC; Leiden University
摘要：We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of wavelet thresholding t...
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作者：Zheng, Qi; Peng, Limin; He, Xuming
作者单位：Emory University; University of Michigan System; University of Michigan
摘要：Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily focuses on the examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may be sensitive to the specific choices of the quantile levels, leading to difficulties in interpre...
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作者：Armstrong, Timothy
作者单位：Yale University
摘要：We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the...
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作者：Ma, Shujie; Carroll, Raymond J.; Liang, Hua; Xu, Shizhong
作者单位：University of California System; University of California Riverside; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney; George Washington University; University of California System; University of California Riverside
摘要：In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the large p small n setting...
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作者：Steinwart, Ingo
作者单位：University of Stuttgart
摘要：The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components. In the case where this algorithm is fed with histogram-based level set estimates, we provide a finite sample analysis, which is then u...
