The Annals of Statistics

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• OPTIMAL PREDICTION IN THE LINEARLY TRANSFORMED SPIKED MODEL AI翻译
  作者：Dobriban, Edgar; Leeb, William; Singer, Amit
  作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities; Princeton University
  摘要：We consider the linearly transformed spiked model, where the observations Y-i are noisy linear transforms of unobserved signals of interest X-i: Y-i = A(i)X(i) + epsilon(i), for i = 1, ..., n. The transform matrices A(i) are also observed. We model the unobserved signals (or regression coefficients) X-i as vectors lying on an unknown low-dimensional space. Given only Y-i and A(i) how should we predict or recover their values? The naive approach of performing regression for each observation sep...
• A FRAMEWORK FOR ADAPTIVE MCMC TARGETING MULTIMODAL DISTRIBUTIONS AI翻译
  作者：Pompe, Emilia; Holmes, Chris; Latuszynski, Krzysztof
  作者单位：University of Oxford; University of Warwick
  摘要：We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution pi and sampling, given the knowledge of the locations of the modes. The sampling algorithm relies on steps of two types: local ones, preserving the mode; and jumps to regions associated with different modes. Besides, the method learns the optimal parameters of the algorithm, while it runs, without requirin...
• ISOTROPIC COVARIANCE FUNCTIONS ON GRAPHS AND THEIR EDGES AI翻译
  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...
• IDENTIFIABILITY OF NONPARAMETRIC MIXTURE MODELS AND BAYES OPTIMAL CLUSTERING AI翻译
  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...
• ADMISSIBLE BAYES EQUIVARIANT ESTIMATION OF LOCATION VECTORS FOR SPHERICALLY SYMMETRIC DISTRIBUTIONS WITH UNKNOWN SCALE AI翻译
  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...
• SINGULARITY, MISSPECIFICATION AND THE CONVERGENCE RATE OF EM AI翻译
  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...
• MINIMAX OPTIMAL SEQUENTIAL HYPOTHESIS TESTS FOR MARKOV PROCESSES AI翻译
  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...
• RELAXING THE ASSUMPTIONS OF KNOCKOFFS BY CONDITIONING AI翻译
  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...
• DOUBLE-SLICING ASSISTED SUFFICIENT DIMENSION REDUCTION FOR HIGH-DIMENSIONAL CENSORED DATA AI翻译
  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...
• ON THE VALIDITY OF THE FORMAL EDGEWORTH EXPANSION FOR POSTERIOR DENSITIES AI翻译
  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...