-
作者：Taylor, J. E.; Worsley, K. J.
作者单位：Stanford University; Universite de Montreal; McGill University
摘要：Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very si...
-
作者：Coeurjolly, Jean-Francois
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0, 1]. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of nonlinear functions of Gaussian ...
-
作者：Delaigle, Aurore; Hall, Peter; Meister, Alexander
作者单位：University of Bristol; University of Melbourne; University of Stuttgart
摘要：In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without it. However, if additional data are available, then it is possible to estimate consistently the unknown error density. Data are seldom available directly on the transformation, but repeated, or replicated, measurements increasingly are becoming available. S...
-
作者：Arias-Castro, Ery; Candes, Emmanuel J.; Helgason, Hannes; Zeitouni, Ofer
作者单位：University of California System; University of California San Diego; California Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0, 1) while under the alternative, there is an unknown path along which random variables have distribution N(mu, 1), mu > 0, and distribution N(0, 1) away from it. For whi...
-
作者：Meng, Xiao-Li
作者单位：Harvard University
-
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...
-
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...
-
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...
-
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 ...
-
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...
