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作者：Juditsky, A; Nemirovski, A
作者单位：Technion Israel Institute of Technology
摘要：We consider the problem of estimating the distance from an unknown signal, observed in a white-noise model, to convex cones of positive/monotone/convex functions. We show that, when the unknown function belongs to a Holder class, the risk of estimating the L-r-distance, 1 less than or equal to r < infinity, from the signal to a cone is essentially the same (up to a logarithmic factor) as that of estimating the signal itself. The same risk bounds hold for the test of positivity, monotonicity an...
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作者：Fan, JQ; Li, RZ
作者单位：Chinese University of Hong Kong; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures per-form as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave penalized likelih...
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作者：Brillinger, DR
作者单位：University of California System; University of California Berkeley
摘要：The contributions of John W. Tukey to time series analysis, particularly spectrum analysis, are reviewed and discussed. The contributions include: methods, their properties, terminology, popularization, philosophy, applications and education. Much of Tukey's early work on spectrum analysis remained unpublished for many years, but the 1959 book by Blackman and Tukey made his approach accessible to a wide audience. In 1965 the Cooley-Tukey paper on the Fast Fourier Transform spurred a rapid chan...
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作者：Brown, LD; Cai, TT; Low, MG; Zhang, CH
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
摘要：This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the white-noise experiments, which provide synthetic observations and synthetic asymptotic solutions from any one of the two experiments with asymptotic prope...
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作者：Yang, GL
作者单位：University System of Maryland; University of Maryland College Park
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作者：Genon-Catalot, V; Laredo, C; Nussbaum, M
作者单位：Universite Gustave-Eiffel; Universite Paris Saclay; INRAE; Cornell University
摘要：We consider a diffusion model of small variance type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model in the sense of asymptotic equivalence of experiments. It is shown that observation of the diffusion process until its first hitting time of level one is a natural model for the purpose of inference on the drift density. The diffusion model can be discretized by the collection of level crossing times for a uniform grid...
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作者：Geiger, D; Heckerman, D
作者单位：Technion Israel Institute of Technology; Microsoft
摘要：We develop simple methods for constructing parameter priors for model choice among directed acyclic graphical (DAG) models. In particular, we introduce several assumptions that permit the construction of parameter priors for a large number of DAG models from a small set of assessments. We then present a method for directly computing the marginal likelihood of every DAG model given a random sample with no missing observations. We apply this methodology to Gaussian DAG models which consist of a ...
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作者：Anderson, TW
作者单位：Stanford University
摘要：When the rank of the autoregression matrix is unrestricted, the maximum likelihood estimator under normality is the least squares estimator. When the rank is restricted, the maximum likelihood estimator is composed of the eigenvectors of the effect covariance matrix in the metric of the error covariance matrix corresponding to the largest eigenvalues [Anderson, T. W. (1951). Ann. Math. Statist. 22 327-351]. The asymptotic distribution of these two covariance matrices under normality is obtaine...
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作者：Richardson, T; Spirtes, P
作者单位：University of Washington; University of Washington Seattle; Florida Institute for Human & Machine Cognition (IHMC)
摘要：This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation, These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.
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作者：Tsybakov, AB
作者单位：Universite Paris Cite; Sorbonne Universite
