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作者：Panaretos, Victor M.; Zemel, Yoav
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random function {Y(x) : x is an element of [0, 1]} corresponds to its random oscillations in the y-axis, typically encapsulated by its (co) variation around a mean level. In contrast, its phase variation refers to fluctuations in the x-axis, often caused by random ti...
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作者：Xu, Min; Chen, Minhua; Lafferty, John
作者单位：University of Pennsylvania; Amazon.com; University of Chicago
摘要：We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that estimates a sum of one-dimensional convex functions, followed by one-dimensional concave regression fits on the residuals. In contrast to previous methods for sparse additive mo...
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作者：Huang, Shiqiong; Jin, Jiashun; Yao, Zhigang
作者单位：Carnegie Mellon University; National University of Singapore
摘要：Given n samples X-1, X-2,...,X-n from N(0, Sigma), we are interested in estimating the p x p precision matrix Omega = Sigma(-)1; we assume Omega is sparse in that each row has relatively few nonzeros. We propose Partial Correlation Screening (PCS) as a new row -by -row approach. To estimate the ith row of Omega, 1 <= i <= p, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a stage -wise algorithm, where in each stage, the algorithm upd...
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作者：Taylor, Jonathan E.; Loftus, Joshua R.; Tibshirani, Ryan J.
作者单位：Stanford University; Carnegie Mellon University
摘要：We derive an exact p-value for testing a global null hypothesis in a general adaptive regression setting. Our approach uses the Kac-Rice formula [as described in Random Fields and Geometry (2007) Springer, New York] applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, group lasso, principal components and matrix completion problems. For...
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作者：Kim, Arlene K. H.; Samworth, Richard J.
作者单位：University of Cambridge
摘要：The estimation of a log-concave density on R-d represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss functions, and adopt a minimax approach. We first show that no statistical procedure based on a sample of size n can estimate a log-concave density with respect to the squared Hellinger loss function with supremum risk smaller than order n(-4/5), when d = ...
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作者：Delaigle, Aurore
作者单位：University of Melbourne; University of Melbourne
摘要：Peter Hall died in Melbourne on January 9, 2016. He was an extremely prolific researcher and contributed to many different areas of statistics. In this paper, I talk about my experience with Peter and I summarise his main contributions to deconvolution, which include measurement error problems and problems in image analysis.
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作者：Samworth, Richard J.
作者单位：University of Cambridge
摘要：In this article, I summarise Peter Hall's contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him. This article complements [Ann. Statist. 44 (2016) 1821-1836; Ann. Statist. 44 (2016) 1837-1853; Ann. Statist. 44 (2016) 1854-1866 and Ann. Statist. 44 (2016) 1867-1887], which focus on other aspects...
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作者：Dette, Holger; Schorning, Kirsten
作者单位：Ruhr University Bochum
摘要：We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal designs are found expl...
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作者：Ma, Shujie; He, Xuming
作者单位：University of California System; University of California Riverside; University of Michigan System; University of Michigan
摘要：Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score test for the index...
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作者：Delaigle, Aurore; Hall, Peter; Zhou, Wen-Xin
作者单位：University of Melbourne; University of Melbourne; Princeton University
摘要：We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general...
