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作者：Li, Jia; Liu, Yunxiao; Xiu, Dacheng
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill; University of Chicago
摘要：We propose semiparametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. A plug-in method that uses nonparametric estimates of spot volatilities is known to induce high-order biases that need to be corrected to obey a central limit theorem. Such bias terms arise from boundary effects, the diffusive and jump movements of stochastic volatility and the sampling error from the nonparametric spot volatility estimation. We propose a n...
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作者：Carpentier, Alexandra; Verzelen, Nicolas
作者单位：Otto von Guericke University; INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier
摘要：Consider the Gaussian vector model with mean value.. We study the twin problems of estimating the number parallel to theta parallel to(0) of nonzero components of. and testing whether parallel to theta parallel to(0) is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of parallel to theta parallel to(0) as a multiple te...
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作者：Bhattacharya, Anirban; Pati, Debdeep; Yang, Yun
作者单位：Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback-Leibler (KL) neighborhood of the true parameter (or the KL divergence minimizer in the misspeci...
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作者：De Castro, Yohann; Gamboa, Fabrice; Henrion, Didier; Hesst, Roxana; Lasserre, Jean-Bernard
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semialgebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This article shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy in...
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作者：Bao, Zhigang; Hu, Jiang; Pan, Guangming; Zhou, Wang
作者单位：Hong Kong University of Science & Technology; Northeast Normal University - China; Nanyang Technological University; National University of Singapore
摘要：Consider a Gaussian vector z = (x', y')', consisting of two sub-vectors x and y with dimensions p and q, respectively. With n independent observations of z, we study the correlation between x and y, from the perspective of the canonical correlation analysis. We investigate the high-dimensional case: both p and q are proportional to the sample size n. Denote by Sigma(uv) the population cross-covariance matrix of random vectors u and v, and denote by Suv the sample counterpart. The canonical cor...
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作者：Sun, Fasheng; Wang, Yaping; Xu, Hongquan
作者单位：Northeast Normal University - China; Northeast Normal University - China; East China Normal University; University of California System; University of California Los Angeles
摘要：Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-...
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作者：Camerlenghi, Federico; Lijoi, Antonio; Orbanz, Peter; Prunster, Igor
作者单位：University of Milano-Bicocca; Bocconi University; Bocconi University; Columbia University
摘要：Hierarchies of discrete probability measures are remarkably popular as nonparametric priors in applications, arguably due to two key properties: (i) they naturally represent multiple heterogeneous populations; (ii) they produce ties across populations, resulting in a shrinkage property often described as sharing of information. In this paper, we establish a distribution theory for hierarchical random measures that are generated via normalization, thus encompassing both the hierarchical Dirichl...
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作者：Dasgupta, Sayan; Goldberg, Yair; Kosorok, Michael R.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Haifa
摘要：We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed approach.
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作者：Lepski, O., V; Willer, T.
作者单位：Aix-Marseille Universite
摘要：We study the problem of nonparametric estimation under L-p-loss, p is an element of[1, infinity), in the framework of the convolution structure density model on R-d. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. The original pointwise selection rule from a family of kernel-type estimators is proposed. For the selected estimator, we prove an L-p-norm oracle inequality and several of its conseque...
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作者：He, Hera Y.; Basu, Kinjal; Zhao, Qingyuan; Owen, Art B.
作者单位：Stanford University; University of Pennsylvania
摘要：It is common for genomic data analysis to use p-values from a large number of permutation tests. The multiplicity of tests may require very tiny p-values in order to reject any null hypotheses and the common practice of using randomly sampled permutations then becomes very expensive. We propose an inexpensive approximation to p-values for two sample linear test statistics, derived from Stolarsky's invariance principle. The method creates a geometrically derived reference set of approximate p-v...
