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作者：Dalalyan, Arnak S.; Salmon, Joseph
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Cite
摘要：We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in nonparametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression, kernel ridge regression, shrinking estimato...
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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 ...
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作者：Li, Jun; Chen, Song Xi
作者单位：Iowa State University; Peking University; Peking University
摘要：We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the large p, small n situations and (ii) without assuming parametric distributions for the ...
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作者：Chen, Dong; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which ...
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作者：Cisewski, Jessi; Hannig, Jan
作者单位：Carnegie Mellon University; University of North Carolina; University of North Carolina Chapel Hill
摘要：While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval...
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作者：Su, Yu-Ru; Wang, Jane-Ling
作者单位：University of California System; University of California Davis; National Cheng Kung University; University of California System; University of California Davis
摘要：There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open...
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作者：Tang, Yu; Xu, Hongquan; Lin, Dennis K. J.
作者单位：Soochow University - China; University of California System; University of California Los Angeles; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method ...
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作者：Zhu, Hongtu; Ibrahim, Joseph G.; Cho, Hyunsoon
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Cook's distance [Technometrics 19 (1977) 15-18] is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross-sectional data. However, for many complex data structures (e.g., longitudinal data), no rigorous approach has been developed to address a fundamental issue: deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data, and the ma...
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作者：Chetelat, Didier; Wells, Martin T.
作者单位：Cornell University
摘要：We consider the problem of estimating the mean vector of a p-variate normal (theta, Sigma) distribution under invariant quadratic loss, (delta - theta)'Sigma(-1) (delta - theta), when the covariance is unknown. We propose a new class of estimators that dominate the usual estimator delta(0)(X) = X. The proposed estimators of theta depend upon X and an independent Wishart matrix S with n degrees of freedom, however, S is singular almost surely when p > n. The proof of domination involves the dev...
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作者：Antognini, Alessandro Baldi; Zagoraiou, Maroussa
作者单位：University of Bologna
摘要：The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. ...
