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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]...
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作者：Belloni, Alexandre; Oliveira, Roberto I.
作者单位：Duke University; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial (ss)-mixing. In particular, model misspecification...
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作者：Overgaard, Morten; Parner, Erik Thorlund; Pedersen, Jan
作者单位：Aarhus University; Aarhus University
摘要：A general asymptotic theory of estimates from estimating functions based on jack-knife pseudo-observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution. Using results in p-variation norms, the theory is applied to important estimators from time-to-event analysis, namely the Kaplan-Meier estimator and the Aalen-Johansen estimator in a competing risks model, and the corresponding estimators of restricted mean surv...
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作者：Atchade, Yves A.
作者单位：University of Michigan System; University of Michigan
摘要：We study the contraction properties of a quasi-posterior distribution (sic)(n, d) obtained by combining a quasi-likelihood function and a sparsity inducing prior distribution on R-d, as both n (the sample size), and d (the dimension of the parameter) increase. We derive some general results that highlight a set of sufficient conditions under which (sic)(n, d) puts increasingly high probability on sparse subsets of R-d, and contracts toward the true value of the parameter. We apply these result...
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作者：Loh, Po-Ling
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalized regression estimators under fairly mild conditions on the error distribution: When the derivative of the loss function is bounded and satisfies a local restricted curvature con...
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作者：Nandy, Preetam; Maathuis, Marloes H.; Richardson, Thomas S.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle
摘要：We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency when the causal st...
