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作者：Zhong, Ping-Shou; Lan, Wei; Song, Peter X. K.; Tsai, Chih-Ling
作者单位：Michigan State University; University of Michigan System; University of Michigan; University of California System; University of California Davis
摘要：In regression analysis with repeated measurements, such as longitudinal data and panel data, structured covariance matrices characterized by a small number of parameters have been widely used and play an important role in parameter estimation and statistical inference. To assess the adequacy of a specified covariance structure, one often adopts the classical likelihood-ratio test when the dimension of the repeated measurements (p) is smaller than the sample size (n). However, this assessment b...
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作者：Wang, Qinwen; Yao, Jianfeng
作者单位：University of Hong Kong
摘要：Consider two p-variate populations, not necessarily Gaussian, with covariance matrices Sigma 1 and Sigma 2, respectively. Let S-1 and S-2 be the corresponding sample covariance matrices with degrees of freedom m and n. When the difference Delta between Sigma l and Sigma 2 is of small rank compared to p, m and n, the Fisher matrix S := S2-1S1 is called a spiked Fisher matrix. When p, m and n grow to infinity proportionally, we establish a phase transition for the extreme eigenvalues of the Fish...
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作者：Wang, Jingshu; Zhao, Qingyuan; Hastie, Trevor; Owen, Art B.
作者单位：University of Pennsylvania; Stanford University
摘要：We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable( s) of interest (e.g., treatment variable, phenotype) and the outcome. Over the past decade, many statistical methods have been proposed to adjust for the confounders in hypothesis testing. We un...
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作者：Basu, Kinjal; Mukherjee, Rajarshi
作者单位：Stanford University
摘要：In a very recent work, Basu and Owen [Found. Comput. Math. 17 (2017) 467-496] propose the use of scrambled geometric nets in numerical integration when the domain is a product of s arbitrary spaces of dimension d having a certain partitioning constraint. It was shown that for a class of smooth functions, the integral estimate has variance O(n(-1-2/d) (log n)(s-1)) for scrambled geometric nets compared to O(n(-1)) for ordinaryMonte Carlo. The main idea of this paper is to expand on the work by ...
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作者：Toulis, Panos; Airoldi, Edoardo M.
作者单位：University of Chicago; Harvard University
摘要：Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly defined. Intuitively, implicit updates shrink standard stochastic gradient descent updates. The amount o...
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作者：Chakraborty, Anirvan; Chaudhuri, Probal
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：Tests based on mean vectors and spatial signs and ranks for a zero mean in one-sample problems and for the equality of means in two-sample problems have been studied in the recent literature for high-dimensional data with the dimension larger than the sample size. For the above testing problems, we show that under suitable sequences of alternatives, the powers of the mean based tests and the tests based on spatial signs and ranks tend to be same as the data dimension tends to infinity for any ...
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作者：Lin, Yuan-Lung; Phoa, Frederick Kin Hing; Kao, Ming-Hung
作者单位：Academia Sinica - Taiwan; Arizona State University; Arizona State University-Tempe
摘要：Functional magnetic resonance imaging (fMRI) is a pioneering technology for studying brain activity in response to mental stimuli. Although efficient designs on these fMRI experiments are important for rendering precise statistical inference on brain functions, they are not systematically constructed. Design with circulant property is crucial for estimating a hemo-dynamic response function (HRF) and discussing fMRI experimental optimality. In this paper, we develop a theory that not only succe...
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作者：Robins, James M.; Li, Lingling; Mukherjee, Rajarshi; Tchetgen, Eric Tchetgen; van der Vaart, Aad
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Sanofi-Aventis; Genzyme Corporation; Stanford University; Leiden University - Excl LUMC; Leiden University
摘要：We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method employs U-statistics that are based on higher-order influence functions of the parameter of interest, which extend ordinary linear influence functions, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method often leads to a bias-variance trade-off, and results in estimators that converge at a slower thanv root n-rate....
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作者：Nickl, Richard; Soehl, Jakob
作者单位：University of Cambridge
摘要：We consider nonparametric Bayesian inference in a reflected diffusion model dX(t) = b(X-t) dt + sigma(Xt) dW(t), with discretely sampled observations X-0, X-Delta , . . . , X-n Delta. We analyse the nonlinear inverse problem corresponding to the low frequency sampling regime where Delta > 0 is fixed and n -> infinity. A general theorem is proved that gives conditions for prior distributions Pi on the diffusion coefficient sigma and the drift function b that ensure minimax optimal contraction r...
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作者：Cardot, Herve; Cenac, Peggy; Godichon-Baggioni, Antoine
作者单位：Universite Bourgogne Europe
摘要：Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with very large samples of high dimensional data. The collected data may be contaminated by noise so that robust location indicators, such as the geometric median, may be preferred to the mean. In this context, an estimator of the geometric median based on a fast and efficient averaged nonlinear stochastic gradient algorithm has been developed by [Bernoulli 19 (2013) 18-43]...
