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作者：Kume, A.; Preston, S. P.; Wood, Andrew T. A.
作者单位：University of Kent; University of Nottingham
摘要：In an earlier paper Kume & Wood (2005) showed how the normalizing constant of the Fisher-Bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation. In this sequel, we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent Fisher-Bingham distributions on Cartesian products of spheres, and Fisher-Bingham distributions on Stiefel manifolds. In each case, ...
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作者：Wang, Xiao; Du, Pang; Shen, Jinglai
作者单位：Purdue University System; Purdue University; Virginia Polytechnic Institute & State University; University System of Maryland; University of Maryland Baltimore County
摘要：This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues arising in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The penalty is a function of the design points in order to accommodate local behaviour of the regression function. We show that the spatially adaptive smoothing spline estimator is approximately...
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作者：Armagan, A.; Dunson, D. B.; Lee, J.; Bajwa, W. U.; Strawn, N.
作者单位：SAS Institute Inc; Duke University; Seoul National University (SNU); Rutgers University System; Rutgers University New Brunswick; Duke University
摘要：We investigate the asymptotic behaviour of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighbourhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions.
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作者：Magirr, D.; Jaki, T.; Posch, M.; Klinglmueller, F.
作者单位：Lancaster University; Medical University of Vienna
摘要：We describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two-stage closed test procedure in an adaptive experiment. The closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will, in general, have a complex, nonrectangular shape. We find the smallest cross-product of simultaneous confidence i...
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作者：Canale, Antonio; Dunson, David B.
作者单位：University of Turin; Duke University
摘要：Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applied contexts, and hierarchical Poisson models make restrictive assumptions about overdispersion in marginal distributions. In this article we propose a class of nonparametric Bay...
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作者：Chen, Kun; Dong, Hongbo; Chan, Kung-Sik
作者单位：University of Connecticut; University of Wisconsin System; University of Wisconsin Madison; University of Iowa
摘要：We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally nonconvex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed nonconvex penalized regression method has a global optimal ...
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作者：Liu, Xiaoxi; Zeng, Donglin
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We study variable selection in general transformation models for right-censored data. The models studied can incorporate external time-varying covariates, and they include the proportional hazards model and the proportional odds model as special cases. We propose an estimation method that involves minimizing a weighted negative partial loglikelihood function plus an adaptive lasso penalty, with the initial values obtained from nonparametric maximum likelihood estimation. The objective function...
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作者：Titterington, D. M.
作者单位：University of Glasgow
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作者：Susko, Edward
作者单位：Dalhousie University
摘要：When the null hypothesis constrains parameters to the boundary of the parameter space, the asymptotic null distribution of the likelihood ratio statistic is often a mixture of chi-squared distributions, giving rise to the so-called chi-bar test, where weights can depend on the true unknown parameter and be difficult to calculate. We consider the test that conditions on the observed number of null hypothesis parameters in the interior of the parameter space. This approach uses simple chi-square...
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作者：Wood, Simon N.
作者单位：University of Bath
摘要：Testing that random effects are zero is difficult, because the null hypothesis restricts the corresponding variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed models, this paper exploits the link between random effects and penalized regression to develop a simple test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates and then to express the likelihood ratio as a readily computed qu...
