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作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Yichao
作者单位：Peking University; University of Colorado System; University of Colorado Denver; North Carolina State University
摘要：We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening proced...
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作者：Johnson, Valen E.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most power...
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作者：Tao, Minjing; Wang, Yazhen; Zhou, Harrison H.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Yale University
摘要：Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Ito process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a volatility matrix est...
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作者：Zheng, Wei
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：In crossover design experiments, the proportional model, where the carryover effects are proportional to their direct treatment effects, has draw attentions in recent years. We discover that the universally optimal design under the traditional model is E-optimal design under the proportional model. Moreover, we establish equivalence theorems of Kiefer-Wolfowitz's type for four popular optimality criteria, namely A, D, E and T (trace).
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作者：Castillo, Ismael; Nickl, Richard
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Cambridge
摘要：Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact 1 - alpha frequentist coverage level and whose L-2-diameter shrinks at the minimax rate of convergence (within logarithmic factors) over Holder balls. Other...
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作者：Lv, Jinchi
作者单位：University of Southern California
摘要：High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one. With the probabilistic view, we establish the concentration property and robust spark bound for large random design matrix generated from elliptical distributions, with the former related to the sure screening property and the latter related to sparse model...
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作者：He, Yangbo; Jia, Jinzhu; Yu, Bin
作者单位：Peking University; Peking University; University of California System; University of California Berkeley
摘要：Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov cha...
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作者：Francq, Christian; Zakoian, Jean-Michel
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite de Lille
摘要：This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1, 1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this f...
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作者：Tsao, Min; Wu, Fan
作者单位：University of Victoria
摘要：We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90-120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full parameter space. The resulting extended empirical likelihood is a natural generalization of the original empirical likelihood to the full parameter space; it has the same asymptotic properties and identically shaped contours as the original empirical likelihoo...
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作者：Draisma, Jan; Kuhnt, Sonja; Zwiernik, Piotr
作者单位：Eindhoven University of Technology; Dortmund University of Technology; University of California System; University of California Berkeley
摘要：Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite exponential transformation families. We reveal this structure by explicitly describing, for any undirected graph, the (maximal) matrix group acting on the space of concentration matrices in the model. The continuous part of this group is captured by a poset n...
