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作者：Chen, Xiaohui
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper studies the Gaussian and bootstrap approximations for the probabilities of a nondegenerate U-statistic belonging to the hyperrectangles in R-d when the dimension d is large. A two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed. Subject to mild moment conditions on the kernel, we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in Rd that decays polynomially in sample size ...
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作者：Belloni, Alexandre; Chernozhukov, Victor; Chetverikov, Denis; Wei, Ying
作者单位：Duke University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; Columbia University
摘要：In this paper, we develop procedures to construct simultaneous confidence bands for (p) over tilde potentially infinite-dimensional parameters after model selection for general moment condition models where p is potentially much larger than the sample size of available data, n. This allows us to cover settings with functional response data where each of the p parameters is a function. The procedure is based on the construction of score functions that satisfy Neyman orthogonality condition appr...
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作者：Hoermann, Siegfried; Kokoszka, Piotr; Nisol, Gilles
作者单位：Graz University of Technology; Colorado State University System; Colorado State University Fort Collins; Universite Libre de Bruxelles
摘要：We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully functional. Generally, fo...
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作者：Huckemann, Stephan F.; Eltzner, Benjamin
作者单位：University of Gottingen
摘要：For sequences of random backward nested subspaces as occur, say, in dimension reduction for manifold or stratified space valued data, asymptotic results are derived. In fact, we formulate our results more generally for backward nested families of descriptors (BNFD). Under rather general conditions, asymptotic strong consistency holds. Under additional, still rather general hypotheses, among them existence of a.s. local twice differentiable charts, asymptotic joint normality of a BNFD can be sh...
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作者：Chang, Ming-Chung; Cheng, Ching-Shui
作者单位：Academia Sinica - Taiwan; University of California System; University of California Berkeley
摘要：In a multi-stratum factorial experiment, there are multiple error terms (strata) with different variances that arise from complicated structures of the experimental units. For unstructured experimental units, minimum aberration is a popular criterion for choosing regular fractional factorial designs. One difficulty in extending this criterion to multi-stratum factorial designs is that the formulation of a word length pattern based on which minimum aberration is defined requires an order of des...
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作者：Butucea, Cristina; Guta, Madalin; Nussbaum, Michael
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Ecole Polytechnique; Universite Paris Saclay; University of Nottingham; Cornell University
摘要：Quantum technology is increasingly relying on specialised statistical inference methods for analysing quantum measurement data. This motivates the development of quantum statistics, a field that is shaping up at the overlap of quantum physics and classical statistics. One of the less investigated topics to date is that of statistical inference for infinite dimensional quantum systems, which can be seen as quantum counterpart of nonparametric statistics. In this paper, we analyse the asymptotic...
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作者：Brown, Lawrence D.; Mukherjee, Gourab; Weinstein, Asaf
作者单位：University of Pennsylvania; University of Southern California; Stanford University
摘要：We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within block but not necessarily between them, as suggested before by Lindley and Smith [J. R. Stat. Soc., B 34 (1972) 1-41]. The hyperparameters of this hierarchical model, instead of considered fixed, are to be substituted with data-dependent values in such a way th...
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作者：Rothenhaeusler, Dominik; Ernest, Jan; Buehlmann, Peter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider identifiability of partially linear additive structural equation models with Gaussian noise (PLSEMs) and estimation of distributionally equivalent models to a given PLSEM. Thereby, we also include robustness results for errors in the neighborhood of Gaussian distributions. Existing identifiability results in the framework of additive SEMs with Gaussian noise are limited to linear and nonlinear SEMs, which can be considered as special cases of PLSEMs with vanishing nonparametric or ...
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作者：Zhao, Junlong; Yu, Guan; Liu, Yufeng
作者单位：Beijing Normal University; State University of New York (SUNY) System; University at Buffalo, SUNY; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：Robustness is a desirable property for many statistical techniques. As an important measure of robustness, the breakdown point has been widely used for regression problems and many other settings. Despite the existing development, we observe that the standard breakdown point criterion is not directly applicable for many classification problems. In this paper, we propose a new breakdown point criterion, namely angular breakdown point, to better quantify the robustness of different classificatio...
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作者：Kim, Arlene K. H.; Guntuboyina, Adityanand; Samworth, Richard J.
作者单位：University of Cambridge; Sungshin Women's University; University of California System; University of California Berkeley
摘要：The log-concave maximum likelihood estimator of a density on the real line based on a sample of size n is known to attain the minimax optimal rate of convergence of O(n(-4/5)) with respect to, for example, squared Hellinger distance. In this paper, we show that it also enjoys attractive adaptation properties, in the sense that it achieves a faster rate of convergence when the logarithm of the true density is k-affine (i.e., made up of k-affine pieces), or close to k-affine, provided in each ca...
