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作者：Meng, Xiao-Li
作者单位：Harvard University
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作者：Paul, Debashis; Bair, Eric; Hastie, Trevor; Tibshirani, Robert
作者单位：University of California System; University of California Davis; Stanford University; Stanford University; Stanford University
摘要：We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a preconditioned response variable. The primary method used for this initial regression is supervised principal components. Then we apply a standard procedure such as forward stepwise selection or the LASSO to the preconditioned response variable. In a number of simulated and real data exampl...
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作者：Clemencon, Stephan; Lugosi, Gabor; Vayatis, Nicolas
作者单位：IMT - Institut Mines-Telecom; IMT Atlantique; Pompeu Fabra University; Universite Paris Saclay
摘要：The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is better, with minimum ranking risk. Since the natural estimates of the risk are of the form of a U-statistic, results of the theory of U-processes are required for investigating the consistency of...
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作者：Fang, X.; Hedayat, A. S.
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a four-parameter composed model is found to be a saturated four-point uniform LD design with the two boundary points of the design space in the LD design support. For a five-parameter composed model, a sufficient condition for the LD design to require the minimum number of sampling time points is derived. Robust LD designs are also in...
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作者：Owen, Art B.
作者单位：Stanford University
摘要：We consider the problem of computing an approximation to the integral I = integral([0, 1])d f (x) dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n(-1/2)) from n independent random function evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully equispaced evaluation points can attain the rate O(n(-1+epsilon)) for any epsilon > 0 and randomized QMC (RQMC) can attain the RMSE O(n(-3/2+epsilon)), both under mild conditions on f. Classical ...
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作者：Van Bellegem, Sebastien; von Sachs, Rainer
作者单位：Universite Catholique Louvain
摘要：We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary, wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on scales. We propose a poi...
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作者：Zou, Hui; Li, Runze
作者单位：University of Minnesota System; University of Minnesota Twin Cities; 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：Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function is computationally challenging, because the objective function is nondifferentiable and nonconcave. In this article, we propose a new unified algorithm based on the local linear approximation (LLA) for maximizing the penalized likelihood for a broad class o...
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作者：Rajaratnam, Bala; Massam, Helene; Carvalho, Carlos M.
作者单位：Stanford University; York University - Canada; University of Chicago
摘要：In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the W-PG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278-1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The W-PG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in diffe...
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作者：Cai, T. Tony; Wang, Lie
作者单位：University of Pennsylvania
摘要：We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. The estimator is shown to achieve the optimal adaptive rate of convergence under the pointwise squared ...
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作者：Cuesta-Albertos, Juan A.; Matran, Carlos; Mayo-Iscar, Agustin
作者单位：Universidad de Cantabria; Universidad de Valladolid
摘要：Robust estimators of location and dispersion are Often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data Outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with Such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censo...
