-
作者：Van de Geer, Sara; Buehlmann, Peter; Ritov, Ya'acov; Dezeure, Ruben
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Hebrew University of Jerusalem
摘要：We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217-242]: we analyze its asymptotic properties and establish its asymptotic optimality in terms of...
-
作者：Zou, Changliang; Yin, Guosheng; Feng, Long; Wang, Zhaojun
作者单位：Nankai University; University of Hong Kong; Nankai University
摘要：In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for det...
-
作者：Jacod, Jean; Reiss, Markus
作者单位：Universite Paris Cite; Sorbonne Universite; Humboldt University of Berlin
摘要：The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous Ito semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the jumps are not summable In this paper, we study this optimal rate, in the minimax sense and for appropriate bounded nonparametric classes of semimartingales. We show that, if the rth powers of the jumps are sununable for some r is an element of [0, 2), the minimax r...
-
作者：Pomatto, Luciano; Al-Najjar, Nabil; Sandroni, Alvaro
作者单位：Northwestern University
摘要：We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the litera...
-
作者：Chakraborty, Anirvan; Chaudhuri, Probal
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The spatial distribution has been widely used to develop various non-parametric procedures for finite dimensional multivariate data. In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach spaces. Many technical difficulties are encountered in such spaces that are primarily due to the noncompactness of the closed unit ball. In this work, we prove some Glivenko-Cantelli and Donsker-type results for the empirical spatial distribution process in i...
-
作者：Genon-Catalot, Valentine; Laredo, Catherine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Paris Saclay; INRAE; Universite Paris Saclay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); INRAE; INRAE; Universite Paris Cite; Universite Paris Saclay
摘要：We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived....
-
作者：Pati, Debdeep; Bhattacharya, Anirban; Pillai, Natesh S.; Dunson, David
作者单位：State University System of Florida; Florida State University; Texas A&M University System; Texas A&M University College Station; Harvard University; Duke University
摘要：Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size. Under relevant sparsity assumptions on the true covariance matrix, we show that commonly-used point mass mixture priors on the fact...
-
作者：Groemping, Ulrike; Xu, Hongquan
作者单位：University of California System; University of California Los Angeles
摘要：The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of R-2 values (based on orthogonal coding) or sums of squared canonical correlations (based on arbitrary coding). Directly related to these results, we derive two versions of general...
-
作者：Fan, Jianqing; Xue, Lingzhou; Zou, Hui
作者单位：Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Minnesota System; University of Minnesota Twin Cities
摘要：Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this importa...
-
作者：Arias-Castro, Ery; Verzelen, Nicolas
作者单位：University of California System; University of California San Diego; INRAE
摘要：We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erdos-Renyi graph with probability p(0). Under the (composite) alternative, there is an unknown subgraph of n nodes where the probability of connection is P-1 > p(0). We derive a detection lower bound for detect...
