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作者：Singh, Aarti; Scott, Clayton; Nowak, Robert
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Michigan System; University of Michigan
摘要：Consider the problem of estimating the gamma-level set G(gamma)* = {x : f(x) > gamma} of an unknown d-dimensional density function f based on n independent observations X(1), ..., X(n) from the density. This problem has been addressed under global error criteria related to the symmetric set difference. However, in certain applications a spatially uniform mode of convergence is desirable to ensure that the estimated set is close to the target set everywhere. The Hausdorff error criterion provid...
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作者：Bickel, Peter J.; Ritov, Ya'acov; Tsybakov, Alexandre B.
作者单位：University of California System; University of California Berkeley; Hebrew University of Jerusalem; Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. Forboth methods, wederive, inparallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the e(p) estimation loss for 1 <= p <= 2 in the linear model when the number of variables can be Much larger than the sample size.
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作者：Chen, Hegang H.; Cheng, Ching-Shui
作者单位：University System of Maryland; University of Maryland Baltimore; University of California System; University of California Berkeley
摘要：It is known that all resolution IV regular 2(n-m) designs of run size N = 2(n-m) where 5N/16 < n < N/2 must be projections of the maximal even design with N/2 factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even 2(n-m) design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration 2(n-m) designs of resolution IV and the structures of their com...
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作者：Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
作者单位：University of Rome Tor Vergata; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Cite
摘要：We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT converaence results for polynomial functionals of the ...
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作者：Chang, Hua-Hua; Ying, Zhiliang
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Columbia University
摘要：Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive design obtained by maxi...
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作者：Gao, Jiti; King, Maxwell; Lu, Zudi; Tjostheim, Dag
作者单位：University of Adelaide; Monash University; Curtin University; University of Bergen
摘要：This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as the choice of a si...
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作者：Lam, Clifford; Fan, Jianqing
作者单位：University of London; London School Economics & Political Science; Princeton University
摘要：This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration p...
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作者：Owen, Art B.
作者单位：Stanford University
摘要：This paper revisits a meta-analysis method proposed by Pearson [Biometrika 26 (1934) 425-442] and first used by David [Biometrika 26 (1934) 1-11]. It was thought to be inadmissible for over fifty years, dating back to a paper of Birnbaum [J. Amer Statist. Assoc. 49 (1954) 559-574]. It turns out that the method Birnbaum analyzed is not the one that Pearson proposed. We show that Pearson's proposal is admissible. Because it is admissible, it has better power than the standard test of Fisher [Sta...
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作者：McNeil, Alexander J.; Neslehova, Johanna
作者单位：Heriot Watt University; University of Edinburgh; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional l(1)-norm symmetric distributions that place no point mass at the origin, The d-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math....
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Northwestern University
摘要：We consider a bivariate process X-t = (X-t(1), X-t(2)), which is observed on a finite time interval [0, T] at discrete times 0, Delta(n), 2 Delta(n), .... Assuming that its two components X-1 and X-2 have jumps on [0, T], we derive tests to decide whether they have at least one jump occurring at the same time (common jumps) or not (disjoint jumps). There are two different tests for the two possible null hypotheses (common jumps or disjoint jumps). Those tests have a prescribed asymptotic level...
