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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...
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作者：Dieuleveut, Aymeric; Bach, Francis
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS H, even if the optimal predictor (i.e., the conditional expectation) is not in H. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorith...
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作者：Qu, Simeng; Wang, Jane-Ling; Wang, Xiao
作者单位：Purdue University System; Purdue University; University of California System; University of California Davis
摘要：Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coe...
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作者：Doss, Charles R.; Wellner, Jon A.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle
摘要：We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on R. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n(-2/5) when -1 < s < infinity where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.
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作者：Kneip, Alois; Poss, Dominik; Sarda, Pascal
作者单位：University of Bonn; University of Bonn; University of Bonn; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：The paper considers functional linear regression, where scalar responses Y1,..., Yn are modeled in dependence of i.i.d. random functions X1,..., Xn. We study a generalization of the classical functional linear regression model. It is assumed that there exists an unknown number of points of impact, that is, discrete observation times where the corresponding functional values possess significant influences on the response variable. In addition to estimating a functional slope parameter, the prob...
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作者：Mukherjee, Sumit
作者单位：Columbia University
摘要：Asymptotics of the normalizing constant are computed for a class of one parameter exponential families on permutations which include Mallows models with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE and a computable approximation of the MLE are shown to be consistent. The pseudo-likelihood estimator of Besag is shown to be root n-consistent. An iterative algorithm (IPFP) is proved to converge to the limiting normalizing constant. The Mallows model with Kendall's tau i...
