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作者：Shah, Rajen D.; Peters, Jonas
作者单位：University of Cambridge; University of Copenhagen
摘要：It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors X and Y are independent, given Z, is a hard statistical problem if Z is a continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests usually have power against ...
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作者：Evans, Robin J.
作者单位：University of Oxford
摘要：We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases-including common classes of causal or graphical models, as well as time series models-distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametr...
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作者：Bhattacharya, Bhaswar B.
作者单位：University of Pennsylvania
摘要：In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum spanning tree and the K-nearest neighbor (NN) graphs, among others. These tests are asymptotically distribution-free, universally consistent and computationally efficient, making them particularly useful in modern applications. However, very little is known abo...
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作者：Donnet, Sophie; Rivoirard, Vincent; Rousseau, Judith
作者单位：INRAE; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First, rates are derived for L-1-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the L-1-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random partitions and priors based on mixtures of Betas distr...
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作者：Berger, James O.; Sun, Dongchu; Song, Chengyuan
作者单位：Duke University; University of Nebraska System; University of Nebraska Lincoln; East China Normal University
摘要：Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this paper, we propose a new class of priors for the covariance matrix, including both inverse Wishart and reference priors as special cases. The main motivation for the new class is to have available priors-both subjective and objective- that do not force eigenvalues apart, which is a criticism of inverse Wishart and Jeffreys priors. Extensive compariso...
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作者：Syring, Nicholas; Martin, Ryan
作者单位：Washington University (WUSTL); North Carolina State University
摘要：Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation. From a statistical point of view, a challenge is that likelihood-based methods require modeling the pixel intensities inside and outside the image boundary, even though these distributions are typically not of interest. Since misspecification of the pixel intensity distributions can negatively affect inference on the image boundary, it would be desirable to avoid thi...
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作者：Konig, Claudia; Munk, Axel; Werner, Frank
作者单位：University of Gottingen
摘要：We consider the problem of finding anomalies in a d-dimensional field of independent random variables {Y-i}(i is an element of{1,...,n}d), each distributed according to a one-dimensional natural exponential family F = {F-theta}(theta is an element of Theta). Given some baseline parameter theta(0) is an element of Theta, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions R those regions R subset of {1, ..., n}(d) with theta(i) not equal thet...
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作者：Han, Yanjun; Jiao, Jiantao; Weissman, Tsachy; Wu, Yihong
作者单位：Stanford University; University of California System; University of California Berkeley; Yale University
摘要：We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates (n ln n.)(-s/(s+d)) + n(-1/2) for 0 < s <= 2 for densities supported on [0, 1](d), where s is the smoothness parameter and n is the number of independent samples. We generalize the results to densities with unbounded support: given an Orlicz functions Psi of rapid growth (such as the subexponential ...
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作者：Karmakar, Bikram; Small, Dylan S.
作者单位：University of Pennsylvania
摘要：An elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis. Statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated. In practice, the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions. This verbal approach can miss quantita...
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作者：Bing, Xin; Bunea, Florentina; Ning, Yang; Wegkamp, Marten
作者单位：Cornell University; Cornell University
摘要：This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix A in a latent factor model X = AZ + E, for an observable random vector X is an element of R-p, with correlated unobservable factors Z is an element of R-K, with K unknown, and uncorrelated noise E. Each row of A is scaled, and allowed to be sparse. In order to identify the loading matrix A, we require the existence of pure variables, which are components of X that are associated, via A...
