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Covariance estimation via fiducial inference

Statistical Theory and Related Fields 2021年第4期5卷 316-331页

作者： W.Jenny Shi Jan Hannig Randy C.S.Lai Thomas C.M.Lee Financial Planning&Analysis MassMutualBostonMAUSA Department of Statistics&Operations Research University of North CarolinaChapel HillNCUSA Department of Statistics University of CaliforniaDavisCAUSA

As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for *** work has been done under the frequentist and Bayesian *** to quantify the uncertainty of the estimators without having to choose a prior,we have developed a fiducial approach to the estimation of covariance *** upon the fiducial Berstein-von Mises Theorem,we show that the fiducial distribution of the covariate matrix is consistent under our ***,the samples generated from this fiducial distri-bution are good estimators to the true covariance matrix,which enable us to define a meaningful confidence region for the covariance ***,we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.

关键词： covariance estimation sparsity fiducial inference cliques

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A fiducial approach to the nonparametric deconvolution problem:The discrete case

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Science China Mathematics 2024年第11期67卷 2653-2670页

作者： Yifan Cui Jan Hannig Center for Data Science Zhejiang University Department of Statistics and Operations Research University of North Carolina at Chapel Hill

fiducial inference is applied to nonparametric g-modeling in the discrete *** propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence *** study the theoretical properties of the fiducial distribution and perform extensive simulations in various *** proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence ***,we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients.

关键词： confidence intervals empirical Bayes fiducial inference nonparametric deconvolution

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GENERALIZED p-VALUES FOR TESTING REGRESSION COEFFICIENTS IN PARTIALLY LINEAR MODELS

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Journal of Systems Science & Complexity 2010年第6期23卷 1118-1132页

作者： Huimin HU Xingzhong XU Guoying LI School of Statistics and Mathematics Shandong University of Finance Jinan 250014 China. Department of Mathematics Beijing Institute of Technology Beijing 100081 China. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.

关键词： fiducial inference frequency property generalized p-value hypothesis testing partially linear model.

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