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作者：Sejdinovic, Dino; Sriperumbudur, Bharath; Gretton, Arthur; Fukumizu, Kenji
作者单位：University of London; University College London; University of Cambridge; Max Planck Society; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a positive definite ke...
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作者：Berthet, Quentin; Rigollet, Philippe
作者单位：Princeton University
摘要：We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on simulated datasets....
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作者：Buecher, Axel; Vetter, Mathias
作者单位：Ruhr University Bochum
摘要：In this paper nonparametric methods to assess the multivariate Levy measure are introduced. Starting from high-frequency observations of a Levy process X, we construct estimators for its tail integrals and the Pareto-Levy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length Delta(n), the rate of convergence is k(n)(-1/2) for k(n) = n Delta(n) which is natural concerning inference on the Levy measure. Besid...
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作者：Jacod, Jean; Podolskij, Mark
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ruprecht Karls University Heidelberg
摘要：In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.
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作者：Schmidt-Hieber, Johannes; Munk, Axel; Duembgen, Lutz
作者单位：Vrije Universiteit Amsterdam; University of Gottingen; Max Planck Society; University of Bern
摘要：We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investi...
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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...
