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作者：Huang, Tzee-Ming
作者单位：National Chengchi University
摘要：In this paper, the maximal nonlinear conditional correlation of two random vectors X and Y given another random vector Z. denoted by rho(1) (X. Y vertical bar Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When Z is continuous, a test for testing the conditional independence of X and Y given Z is constructed based on the estimator of a weighted average of the form Sigma(nZ)(k=1) f(Z)(z(k))rho(2)(1) (X, Y vertical bar Z = z(k)). where f(Z) ...
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作者：Liu, Weidong; Wu, Wei Biao
作者单位：University of Pennsylvania; University of Chicago
摘要：We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression function...
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作者：Brown, Lawrence D.; Cai, T. Tony; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function, which include, for example, Poisson regression, binomial regression and gamma regression. We pro...
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作者：Huckemann, Stephan F.; Kim, Peter T.; Koo, Ja-Yong; Munk, Axel
作者单位：University of Gottingen; University of Guelph; Korea University
摘要：In this paper we consider a novel statistical inverse problem on the Poincare, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of 2 x 2 real matrices of determinant one via Mobius transformations. Our approach is based on a deconvolution technique which relies on the Helgason-Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density th...
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作者：Moreno, Elias; Javier Giron, F.; Casella, George
作者单位：University of Granada; Universidad de Malaga; State University System of Florida; University of Florida
摘要：In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer Statist. Assoc. 104 (2009) 1261-1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not totally understood. Here we study consistency of the Bayes factors for nested normal linear models when...
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作者：Kim, Min Hee; Akritas, Michael G.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of the threshold parameter. This results in improved power over the soft and hard thresholding methods. Moreover, order thresholding is not restricted to the normal distribution. An extension of the basic order threshold statistic to high-dimensional ANOVA is p...
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作者：McKeague, Ian W.; Sen, Bodhisattva
作者单位：Columbia University; Columbia University
摘要：This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a sensitive time point, is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-similar) properties in common with a fractional Brownian motion with an unknown Hurst exponent. Bootstr...
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作者：Du, Pang; Ma, Shuangge; Liang, Hua
作者单位：Virginia Polytechnic Institute & State University; Yale University; University of Rochester
摘要：We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate effect function, pro...
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作者：Drees, Holger; Rootzen, Holger
作者单位：University of Hamburg; Chalmers University of Technology; University of Gothenburg
摘要：Let (X-n, i) 1 <= i <= n,m is an element of N be a triangular array of row-wise stationary R-d-valued random variables. We use a blocks method to define clusters of extreme values: the rows of (X-n, i) are divided into m(n) blocks (Y-n, j), and if a block contains at least one extreme value, the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. The main results are uniform central limit theorems for empirical processe...
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作者：Zhou, Zhou
作者单位：University of Toronto
摘要：The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the a...
