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作者：Hilgert, Nadine; Mas, Andre; Verzelen, Nicolas
作者单位：INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier
摘要：We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional principal component analysis. Interestingly, the procedures are completely data-driven and do not require any prior knowledge on the smoothness of the slope nor on the smoothness of the covariate functions. The levels and powers against local alternatives are as...
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作者：Uhler, Caroline; Raskutti, Garvesh; Buehlmann, Peter; Yu, Bin
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Berkeley
摘要：Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In c...
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作者：Ma, Yanyuan; Zhu, Liping
作者单位：Texas A&M University System; Texas A&M University College Station; Shanghai University of Finance & Economics; Shanghai University of Finance & Economics
摘要：We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing a...
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作者：He, Xuming; Wang, Lan; Hong, Hyokyoung Grace
作者单位：University of Michigan System; University of Michigan; University of Minnesota System; University of Minnesota Twin Cities; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System
摘要：We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline approximations to mo...
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作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Yichao
作者单位：Peking University; University of Colorado System; University of Colorado Denver; North Carolina State University
摘要：We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening proced...
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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).
