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作者：Nussbaum, Michael; Szkola, Arleta
作者单位：Cornell University
摘要：We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finite-dimensional quantum system. A special case is the problem of discriminating between r probability measures on a finite sample space, using n i.i.d. observations. In this classical setting, it is known that the averaged error probability decreases exponentially with exponent given by the worst case binary Chernoff bound between any possible pair of the r pro...
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作者：Huang, Jian; Ma, Shuangge; Li, Hongzhe; Zhang, Cun-Hui
作者单位：University of Iowa; Yale University; University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
摘要：We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouraging sparsity and Laplacian quadratic penalty for promoting smoothness among coefficients associated wit...
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作者：Cai, Juan-Juan; Einmahl, John H. J.; De Haan, Laurens
作者单位：Tilburg University; Universidade de Lisboa; Tilburg University
摘要：When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form {z is an element of R-d : f (z) <= beta}, where f is the joint density and beta a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given...
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作者：Chen, S.; Dick, J.; Owen, A. B.
作者单位：Stanford University; University of New South Wales Sydney
摘要：The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than lid. U(0, 1) points sho...
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作者：Ding, Ying; Nan, Bin
作者单位：University of Michigan System; University of Michigan
摘要：In many semiparametric models that are parameterized by two types of parameters-a Euclidean parameter of interest and an infinite-dimensional nuisance parameter-the two parameters are bundled together, that is, the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the unspecified error distribution function involves the regression coefficients. Motivated by developing ...
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作者：Bickel, Peter J.; Chen, Aiyou; Levina, Elizaveta
作者单位：University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated; University of Michigan System; University of Michigan
摘要：Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average...
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作者：Hall, Peter; Tung Pham; Wand, M. P.; Wang, S. S. J.
作者单位：University of Melbourne; University of Wollongong; University of Technology Sydney
摘要：We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and...
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作者：Ilmonen, Pauliina; Paindaveine, Davy
作者单位：Aalto University; Universite Libre de Bruxelles; Universite Libre de Bruxelles; Tampere University; Sorbonne Universite
摘要：We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = Lambda Z + mu, where mu is a p-vector, Lambda is a full-rank p x p matrix and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Lambda. On the basis of n i.i.d. copies of X, we develop, under a sym...
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作者：Kreiss, Jens-Peter; Paparoditis, Efstathios; Politis, Dimitris N.
作者单位：Braunschweig University of Technology; University of Cyprus; University of California System; University of California San Diego
摘要：We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. ...
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作者：Zhang, Runchu; Phoa, Frederick K. H.; Mukerjee, Rahul; Xu, Hongquan
作者单位：Nankai University; Nankai University; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; University of California System; University of California Los Angeles; Academia Sinica - Taiwan; Northeast Normal University - China
摘要：The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level ...
