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作者：Feng, Xingdong; He, Xuming
作者单位：Shanghai University of Finance & Economics; Shanghai University of Finance & Economics; University of Michigan System; University of Michigan
摘要：The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the ...
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作者：Bhaskar, Anand; Song, Yun S.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS f...
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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....
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作者：Du, Lilun; Zhang, Chunming
作者单位：University of Wisconsin System; University of Wisconsin Madison; Nankai University
摘要：In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value, (p(1), p(2)), for each hypothesis, where pi is a preliminary p-value from prior information and p(2) is the primary p-value for the ultimate analysis. To fi...
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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...
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作者：Sun, Yan; Yan, Hongjia; Zhang, Wenyang; Lu, Zudi
作者单位：Shanghai University of Finance & Economics; University of York - UK; University of Southampton
摘要：Stimulated by the Boston house price data, in this paper, we propose a semiparametric spatial dynamic model, which extends the ordinary spatial autoregressive models to accommodate the effects of some covariates associated with the house price. A profile likelihood based estimation procedure is proposed. The asymptotic normality of the proposed estimators are derived. We also investigate how to identify the parametric/nonparametric components in the proposed semiparametric model. We show how m...
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作者：Lecue, Guillaume; Rigollet, Philippe
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Princeton University
摘要：We consider a general supervised learning problem with strongly convex and Lipschitz loss and study the problem of model selection aggregation. In particular, given a finite dictionary functions (learners) together with the prior, we generalize the results obtained by Dai, Rigollet and Zhang [Ann. Statist. 40 (2012) 1878-1905] for Gaussian regression with squared loss and fixed design to this learning setup. Specifically, we prove that the Q-aggregation procedure outputs an estimator that sati...
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作者：Lockhart, Richard; Taylor, Jonathan; Tibshirani, Ryan J.; Tibshirani, Robert
作者单位：Simon Fraser University; Stanford University; Carnegie Mellon University; Carnegie Mellon University; Stanford University
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作者：Maire, Florian; Douc, Randal; Olsson, Jimmy
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Royal Institute of Technology
摘要：In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different 7-reversible Markov transition kernels P and Q. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels Pi and Q(i), i is an element of {0, 1}, as soon as the kernels of each pair (P-0, P-1) and (Q(0), Q(1)) can be ordered in the sense of...
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作者：Schmidt-Hieber, Johannes
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an experiment, where the anti-derivative of the regression function is continuously observed under additive perturbation by a fractional Brownian motion. Based on a reformulation of the problem using reproducing kernel Hilbert spaces, we derive abstract approximation...
