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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：Berk, Richard; Brown, Lawrence; Buja, Andreas; Zhang, Kai; Zhao, Linda
作者单位：University of Pennsylvania
摘要：It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid post-selection inference by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention interv...
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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; RWTH Aachen University; Cardiff University
摘要：In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the case of dependent data. If the regression functions are eigenfunctions of an integral operator defined by the covariance kernel, it is shown t...
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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：Bien, Jacob; Taylor, Jonathan; Tibshirani, Robert
作者单位：Cornell University; Cornell University; Stanford University; Stanford University
摘要：We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy holds with probability one and derive an unbiased estimate for the degrees of freedom of our estimator. A bound on this estimate reveals the amount of fitting saved by the hiera...
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作者：Zhang, Xianyang; Shao, Xiaofeng
作者单位：University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based t-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new boot...
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作者：Wang, Lan; Kim, Yongdai; Li, Runze
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Seoul National University (SNU); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not gua...
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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...
