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作者：Nguyen, XuanLong; Wainwright, Martin J.; Jordan, Michael I.
作者单位：Duke University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：The goal of binary classification is to estimate a discriminant function gamma from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available directly but are transformed by a dimensionality-reducing quantizer Q. We present conditions on loss functions such that empirical risk minimization yields Bayes consistency when both the discriminant function and the quantizer are estimated. These conditions ar...
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作者：Drton, Mathias
作者单位：University of Chicago
摘要：Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic Subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theorem hold for semi-algebraic sets such that the asymptotics are determined by the tangent cone at the tr...
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作者：Wang, Huixia Judy; Fygenson, Mendel
作者单位：North Carolina State University; University of Southern California
摘要：We develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants. We consider a semi-parametric quantile regression model that makes no distributional assumptions. Our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit. In such studies the focus is often on testing hypotheses about treatment equality. To this end, we propose a ra...
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作者：Berger, James O.; Bernardo, Jose M.; Sun, Dongchu
作者单位：Duke University; University of Missouri System; University of Missouri Columbia
摘要：Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an ex...
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作者：May, Caterina; Flournoy, Nancy
作者单位：University of Milan; University of Eastern Piedmont Amedeo Avogadro; University of Missouri System; University of Missouri Columbia
摘要：This paper illustrates asymptotic properties for a response-adaptive design generated by a two-color, randomly reinforced urn model. The design considered is optimal in the sense that it assigns patients to the best treatment, with probability converging to one. An approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one. Results on the rate of convergence of t...
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作者：Xie, Huiliang; Huang, Jian
作者单位：University of Miami; University of Iowa
摘要：We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneou...
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作者：Steinwart, Ingo; Anghel, Marian
作者单位：United States Department of Energy (DOE); Los Alamos National Laboratory
摘要：We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that Support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if (a) the unknown observational noise process is bounded and has a summable alpha-mixing rate and (b) the unknown ergodic dynamical system is defined by a Lipschitz continuous f...
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作者：Olszewski, Wojciech; Sandroni, Alvaro
作者单位：Northwestern University; University of Pennsylvania; Northwestern University
摘要：A test is said to control for type I error if it is unlikely to reject the data-generating process. However, if it is possible to produce stochastic processes at random such that, for all possible future realizations of the data, the selected process is unlikely to be rejected, then the test is said to be manipulable. So, a manipulable test has essentially no capacity to reject a strategic expert. Many tests proposed in the existing literature, including calibration tests, control for type I e...
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作者：Cai, T. Tony; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the dense and sparse ca...
