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作者：Anderes, Ethan; Moller, Jesper; Rasmussen, Jakob G.
作者单位：University of California System; University of California Davis; Aalborg University
摘要：We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, that is, graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called th...
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作者：Aragam, Bryon; Dan, Chen; Xing, Eric P.; Ravikumar, Pradeep
作者单位：University of Chicago; Carnegie Mellon University
摘要：Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework involving clustering overfitted parametric (i.e., misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature and are flexible enough to include, for example, mixtures of infinite Gaussian mixtures. In contrast to the recent literature, we allow for general nonparametr...
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作者：Maruyama, Yuzo; Strawderman, William E.
作者单位：University of Tokyo; Rutgers University System; Rutgers University New Brunswick
摘要：This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form f (x, u) = eta((p+ n)/2) f (eta{parallel to x - theta parallel to(2) + parallel to u parallel to(2)}), where. is unknown. We show that the natural estimator x is admissible for p = 1, 2. Also, for p >= 3, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of th...
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作者：Dwivedi, Raaz; Nhat Ho; Khamaru, Koulik; Wainwright, Martin J.; Jordan, Michael, I; Yu, Bin
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include suitably separated Gaussian mixture models and mixtures of linear regressions. We consider over-specified settings in which the number of fitted components is larger than the number of components in the true distribution. Such mis-specified settings can lead t...
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作者：Fauss, Michael; Zoubir, Abdelhak M.; Poor, H. Vincent
作者单位：Technical University of Darmstadt; Princeton University
摘要：Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited, and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a g...
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作者：Huang, Dongming; Janson, Lucas
作者单位：Harvard University
摘要：The recent paper Candes et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018) 551-577) introduced model-X knockoffs, a method for variable selection that provably and nonasymptotically controls the false discovery rate with no restrictions or assumptions on the dimensionality of the data or the conditional distribution of the response given the covariates. The one requirement for the procedure is that the covariate samples are drawn independently and identically from a precisely-known (bu...
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作者：Ding, Shanshan; Qian, Wei; Wang, Lan
作者单位：University of Delaware; University of Miami
摘要：This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time T depends on a high-dimensional covariate vector X through low-dimensional linear combinations of covariates Gamma(T) X. The censoring time is allowed to be conditionally independent of the survival time given...
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作者：Kolassa, John E.; Kuffner, Todd A.
作者单位：Rutgers University System; Rutgers University New Brunswick; Washington University (WUSTL)
摘要：We consider a fundamental open problem in parametric Bayesian theory, namely the validity of the formal Edgeworth expansion of the posterior density. While the study of valid asymptotic expansions for posterior distributions constitutes a rich literature, the validity of the formal Edgeworth expansion has not been rigorously established. Several authors have claimed connections of various posterior expansions with the classical Edgeworth expansion, or have simply assumed its validity. Our main...
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作者：Fang, Ethan X.; Ning, Yang; Li, Runze
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Cornell University
摘要：This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low-dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inferenc...
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作者：Porter, Thomas; Stewart, Michael
作者单位：University of Melbourne; University of Sydney
摘要：Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small p-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the 'tailor-made' parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this 'narrow' model. We develop a higher-order framework for analysing the power of th...
