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作者：Bayarri, M. J.; Berger, J. O.; Forte, A.; Garcia-Donato, G.
作者单位：University of Valencia; Duke University; Universitat Jaume I; Universidad de Castilla-La Mancha
摘要：In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the ...
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作者：Durot, Cecile; Kulikov, Vladimir N.; Lopuhaa, Hendrik P.
作者单位：Delft University of Technology
摘要：Let f be a nonincreasing function defined on [0, 1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between f and its Grenander-type estimator on sub-intervals of [0, 1]. The rate of convergence is found to be of order (n/logn)(-1/3) and the limiting distribution to be Gumbel.
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作者：Ingster, Yuri I.; Sapatinas, Theofanis; Suslina, Irina A.
作者单位：Saint Petersburg State Electrotechnical University; University of Cyprus; ITMO University
摘要：Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with l(q)-ellipsoids (bodies), q is an element of (0, 2], for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax rate-opti...
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作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley
摘要：Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization p...
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作者：Zhang, Ting; Wu, Wei Biao
作者单位：University of Iowa; University of Chicago
摘要：We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a n(1/2)-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion ...
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：This paper studies the identification of the Levy jump measure of a discretely-sampled semimartingale. We define successive Blumenthal-Getoor indices of jump activity, and show that the leading index can always be identified, but that higher order indices are only identifiable if they are sufficiently close to the previous one, even if the path is fully observed. This result establishes a clear boundary on which aspects of the jump measure can be identified on the basis of discrete observation...
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作者：Dai, Dong; Rigollet, Philippe; Zhang, Tong
作者单位：Rutgers University System; Rutgers University New Brunswick; Princeton University
摘要：Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by the mean squared error at the design points. While procedures based on exponential weights are known to solve the problem of model selection aggregation in expectation, they are,...
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作者：Lee, Young K.; Mammen, Enno; Park, Byeong U.
作者单位：Kangwon National University; University of Mannheim; Seoul National University (SNU)
摘要：This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition we give a general ...
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作者：Hu, Yanqing; Hu, Feifang
作者单位：University of Virginia
摘要：Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics and metabolomics). Stratified permuted block randomization and minimization methods [Pocock and Simon Biometrics 31 (1975) 103-115, etc.] are the two most popular approaches in practice. However, stratified permuted block randomization fails ...
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作者：Qiu, Yumou; Chen, Song Xi
作者单位：Iowa State University; Peking University; Peking University
摘要：Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Sigma, we propose a test for Sigma being banded with possible diverging bandwidth. The test is adaptive to the large p, small n situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator are investigated by theoretical ...
