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作者：Yuan, Ying; Zhu, Hongtu; Lin, Weili; Marron, J. S.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：Local polynomial regression has received extensive attention for the non-parametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The primary motivation and applicatio...
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作者：Fan, Jianqing; Feng, Yang; Tong, Xin
作者单位：Princeton University; Columbia University; Princeton University
摘要：For high dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and accumulation of noise. Therefore, researchers proposed independence rules to circumvent the diverging spectra, and sparse independence rules to mitigate the issue of accumulation of noise. However, in biological applications, often a group of correlated genes are responsible for clinical outcomes, and the use of the covariance information...
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作者：Allen, Genevera I. I.; Tibshirani, Robert
作者单位：Baylor College of Medicine; Rice University; Stanford University; Rice University
摘要：We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Many of these data matrices are transposable meaning that neither the row variables nor the column variables can be considered independent instances. An example of this scenario is detecting significant genes in microarrays when the samples may be dependent because of latent variables or unknown batch effects. By modelling this matrix data by using the matrix variate normal distribu...
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作者：Farrington, C. Paddy; Unkel, Steffen; Anaya-Izquierdo, Karim
作者单位：Open University - UK; University of London; London School of Hygiene & Tropical Medicine; Open University - UK
摘要：The relative frailty variance among survivors provides a readily interpretable measure of how the heterogeneity of a population, as represented by a frailty model, evolves over time. We discuss the properties of the relative frailty variance, show that it characterizes frailty distributions and that, suitably rescaled, it may be used to compare patterns of dependence across models and data sets. In shared frailty models, the relative frailty variance is closely related to the cross-ratio funct...
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作者：Thas, Olivier; Neve, Jan De; Clement, Lieven; Ottoy, Jean-Pierre
作者单位：Ghent University; University of Wollongong; Ghent University
摘要：We present a semiparametric statistical model for the probabilistic index which can be defined as P(Y <= Y*), where Y and Y* are independent random response variables associated with covariate patterns X and X* respectively. A link function defines the relationship between the probabilistic index and a linear predictor. Asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory. The model is illustrated with several e...
