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作者：Velasco, Carlos; Lobato, Ignacio N.
作者单位：Universidad Carlos III de Madrid; Instituto Tecnologico Autonomo de Mexico
摘要：This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existi...
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作者：Evans, Robin J.
作者单位：University of Oxford
摘要：Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper, we provide a complete algebraic characterization of these models when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular, these two models h...
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作者：Chang, Jinyuan; Guo, Bin; Yao, Qiwei
作者单位：Southwestern University of Finance & Economics - China; Southwestern University of Finance & Economics - China; University of London; London School Economics & Political Science
摘要：We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a p-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore, those lower-dimensional series can be analyzed separately as far as the linear dynamic structure is concerned. Techn...
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作者：Dalalyan, Arnak S.; Grappin, Edwin; Paris, Quentin
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Saclay; HSE University (National Research University Higher School of Economics)
摘要：In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is reasonable to use the Laplace distribution as a prior. The resulting estimator and, specifically, a particular instance of it referred to as the Bayesian lasso, was already used in the statistical literature because of its computational convenience, even though...
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作者：Kong, Xin-Bing
作者单位：Nanjing Audit University
摘要：In this paper, we separate the integrated (spot) volatility of an individual Ito process into integrated (spot) systematic and idiosyncratic volatilities, and estimate them by aggregation of local factor analysis (localization) with large-dimensional high-frequency data. We show that, when both the sampling frequency n and the dimensionality p go to infinity and p >= C root n for some constant C, our estimators of High dimensional Ito process; common driving process; specific driving process, ...
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作者：Lecue, Guillaume; Mendelson, Shahar
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Technion Israel Institute of Technology; Australian National University; Institut Polytechnique de Paris; ENSAE Paris
摘要：We obtain bounds on estimation error rates for regularization procedures of the form (f) over cap is an element of argmin(f is an element of F)(1/N Sigma(N)(i=1) (Yi - f (X-i))(2) + lambda Psi(f)) when Psi is a norm and F is convex. Our approach gives a common framework that may be used in the analysis of learning problems and regularization problems alike. In particular, it sheds some light on the role various notions of sparsity have in regularization and on their connection with the size of...
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作者：Qiu, Yumou; Chen, Song Xi; Nettleton, Dan
作者单位：University of Nebraska System; University of Nebraska Lincoln; Peking University; Peking University; Iowa State University
摘要：Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint signals in high-dimensional response variables. We address the signal detection problem under a general framework, which includes generalized linear models for count-valued responses as special cases. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the signals, based on a...
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作者：Cai, T. Tony; Zhang, Anru
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison
摘要：Perturbation bounds for singular spaces, in particularWedin's sin Theta theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius sin Theta distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rate-optimal, are also given. The new perturbation bounds are appli...
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作者：Collier, Olivier; Comminges, Laetitia; Tsybakov, Alexandre B.; Verzelen, Nicolas
作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Ecole Polytechnique; INRAE
摘要：We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta is an element of R-d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a nonasymptotic rate of convergence that differs from the minimax rate at most by a logarithmic factor. We also show that this optimal adaptive rate cannot be improved when s is unknown. Furthermore, we address the issue of simultaneous adaptation to s and...
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作者：Godolphin, Janet
作者单位：University of Surrey
摘要：Designs with blocks of size two have numerous applications. In experimental situations where observation loss is common, it is important for a design to be robust against breakdown. For designs with one treatment factor and a single blocking factor, with blocks of size two, conditions for connectivity and robustness are obtained using combinatorial arguments and results from graph theory. Lower bounds are given for the breakdown number in terms of design parameters. For designs with equal or n...
