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作者：Cai, Tony; Yuan, Ming
作者单位：University of Pennsylvania; University System of Georgia; Georgia Institute of Technology
摘要：Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by care...
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作者：Xue, Lingzhou; Zou, Hui; Cai, Tianxi
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Harvard University
摘要：The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an approach is computati...
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作者：Arias-Castro, Ery; Bubeck, Sebastien; Lugosi, Gabor
作者单位：University of California System; University of California San Diego; Princeton University; Pompeu Fabra University; ICREA
摘要：We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of possibly correlated se...
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作者：Colombo, Diego; Maathuis, Marloes H.; Kalisch, Markus; 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 problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI ...
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作者：Dette, Holger; Melas, Viatcheslav B.; Shpilev, Petr
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：This paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree n - 2 and n. In a fundamental paper, Atkinson and Fedorov [Biometrika 62 (1975a) 57-70] proposed the T-optimality criterion for this purpose. Recently, Atkinson [MODA 9, Advances in Model-Oriented Design and Analysis (2010) 9-16] determined T-optimal designs for polynomials up to degree 6 numerically and based on these results he conjectured that the suppo...
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作者：Lahiri, Soumendra N.; Mukhopadhyay, Subhadeep
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely de...
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作者：Pillai, Natesh S.; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：Let (X) over tilde (MxN) be a rectangular data matrix with independent real-valued entries [(x) over tilde (ij)] satisfying E (x) over tilde (ij) = 0 and E (x) over tilde (2)(ij) = 1/M, N, M -> infinity. These entries have a subexponential decay at the tails. We will be working in the regime N/M = d(N), lim(N ->infinity) d(N) not equal 0, 1, infinity. In this paper we prove the edge universality of correlation matrices X-dagger X, where the rectangular matrix X (called the standardized matrix)...
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作者：Liu, Jingchen; Xu, Gongjun
作者单位：Columbia University
摘要：In this paper, we derive tail approximations of integrals of exponential functions or Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple applications such as hypothesis testing for spatial models and financial applications.
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作者：Foygel, Rina; Draisma, Jan; Drton, Mathias
作者单位：University of Chicago; Eindhoven University of Technology
摘要：A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation m...
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作者：Tchetgen, Eric J. Tchetgen; Shpitser, Ilya
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard T.H. Chan School of Public Health
摘要：While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon evaluating the total effect of the exposure, investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure, through a mediator...
