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作者：Chen, Song Xi; Gao, Jiti; Tang, Cheng Yong
作者单位：Iowa State University; University of Western Australia
摘要：We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L-2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth choice, the final t...
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作者：Linton, Oliver; Sperlich, Stefan; Van Keilegom, Ingrid
作者单位：University of London; London School Economics & Political Science; University of Gottingen; Universite Catholique Louvain
摘要：This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parame...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely used techniques, in particular in principal component analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample size, n, is of the same order of magnitude as the number of variables p. Random matrix theory pred...
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作者：Bellon, Alexandre; Didier, Gustavo
作者单位：Duke University; Tulane University
摘要：In this paper we provide a provably convergent algorithm for the multi-variate Gaussian Maximum Likelihood version of the Behrens-Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and Richards [5]. Instead of focusing on the first order optimality conditions, the algorithm aims directly for the maximization of the log-likelihood function itself to achieve a global solution. Convergence proof and complexity estimates are provided for the algorith...
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作者：Hofmann, Thomas; Schoelkopf, Bernhard; Smola, Alexander J.
作者单位：Technical University of Darmstadt; Max Planck Society; NICTA
摘要：We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on...
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作者：Rohde, Angelika
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Within the nonparametric regression model with unknown regression function l and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis l = 0 against a nonparametric alternative is proposed. This test is distribution-free and exact for finite samples even in the heteroscedastic case. It adapts in a certain sense to the unknown smoothness of the regression function under the alternative, and it is uniformly co...
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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...
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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 ...
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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...
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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...
