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作者：Rohde, Angelika; Tsybakov, Alexandre B.
作者单位：University of Hamburg; Institut Polytechnique de Paris; ENSAE Paris
摘要：Suppose that we observe entries or, more generally, linear combinations of entries of an unknown m x T-matrix A corrupted by noise. We are particularly interested in the high-dimensional setting where the number mT of unknown entries can be much larger than the sample size N. Motivated by several applications, we consider estimation of matrix A under the assumption that it has small rank. This can be viewed as dimension reduction or sparsity assumption. In order to shrink toward a low-rank rep...
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作者：Douc, Randal; Robert, Christian P.
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
摘要：Casella and Robert [Biometrika 83 (1996) 81-94] presented a general Rao-Blackwellization principle for accept-reject and Metropolis-Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis-Hastings-based estimators while keeping the computation cost under control. We est...
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作者：Chang, Jinyuan; Chen, Song Xi
作者单位：Peking University; Peking University; Iowa State University
摘要：The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Ait-Sahalia [J. Finance 54 (1999) 1361-1395; Econometrica 70 (2002) 223-262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on Ait-Sahalia's [Econometrica 70 (2002) 223-262; A...
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作者：Kolassa, John; Robinson, John
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Sydney
摘要：We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order 1/n. I...
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作者：Khare, Kshitij; Hobert, James P.
作者单位：State University System of Florida; University of Florida
摘要：The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo algorithm that is easy to implement but often suffers from slow convergence. The sandwich algorithm is an alternative that can converge much faster while requiring roughly the same computational effort per iteration. Theoretically, the sandwich algorithm always converges at least as fast as the corresponding DA algorithm in the sense that parallel to K*parallel to <= parallel to K parallel to, where K and K* are the...
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作者：Belloni, Alexandre; Winkler, Robert L.
作者单位：Duke University
摘要：This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study s...
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作者：Bunea, Florentina; She, Yiyuan; Wegkamp, Marten H.
作者单位：State University System of Florida; Florida State University
摘要：We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model. The rank of the RSC estimator provides a consistent estimator of the rank of the coefficient matrix; in general, the rank of our estimator is a co...
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作者：Drton, Mathias; Foygel, Rina; Sullivant, Seth
作者单位：University of Chicago; North Carolina State University
摘要：Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity ...
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作者：Douc, Randal; Moulines, Eric; Olsson, Jimmy; van Handel, Ramon
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Lund University; Princeton University
摘要：Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is strongly consistent under a rather minimal set of assumptions. As special cases of our main result, we obtain consistency in a large class of nonlinear state space models, as well as general results on linear Gaussian state space models and finite state models....
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作者：Haaland, Ben; Qian, Peter Z. G.
作者单位：National University of Singapore; National University of Singapore; University of Wisconsin System; University of Wisconsin Madison
摘要：Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and numeric portions. Boun...
