As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for decades.Much work has been done under the frequentist and Bayesian frameworks.Aiming to quantify the uncertaint...As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for decades.Much work has been done under the frequentist and Bayesian frameworks.Aiming to quantify the uncertainty of the estimators without having to choose a prior,we have developed a fiducial approach to the estimation of covariance matrix.Built upon the Fiducial Berstein-von Mises Theorem,we show that the fiducial distribution of the covariate matrix is consistent under our framework.Consequently,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 matrix.Lastly,we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.展开更多
Fiducial inference is applied to nonparametric g-modeling in the discrete case.We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point...Fiducial inference is applied to nonparametric g-modeling in the discrete case.We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals.We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios.The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals.Furthermore,we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients.展开更多
In this paper,we propose generalized fiducial methods and construct four generalized p-values to test the existence of quantitative trait locus effects under phenotype distributions from a location-scale family.Compar...In this paper,we propose generalized fiducial methods and construct four generalized p-values to test the existence of quantitative trait locus effects under phenotype distributions from a location-scale family.Compared with the likelihood ratio test based on simulation studies,our methods perform better at controlling type I errors while retaining comparable power in cases with small or moderate sample sizes.The four generalized fiducial methods support varied sce-narios:two of them are more aggressive and powerful,whereas the other two appear more conservative and robust.A real data example involving mouse blood pressure is used to illustrate our proposed methods.展开更多
In this study,the authors proposed upper tolerance limits for the gamma mixture distribution based on generalized fiducial inference,and an MCMC simulation is performed to sample from the generalized fiducial distribu...In this study,the authors proposed upper tolerance limits for the gamma mixture distribution based on generalized fiducial inference,and an MCMC simulation is performed to sample from the generalized fiducial distributions.The simulation results and a real hydrological data example show that the proposed tolerance limits are more efficient.展开更多
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 a...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.展开更多
The authors should be congratulated on a stimulating piece of work.There is definitely a great need to understand information-based criteria such as BIC better.I especially especially enjoyed the way they simplified t...The authors should be congratulated on a stimulating piece of work.There is definitely a great need to understand information-based criteria such as BIC better.I especially especially enjoyed the way they simplified the problem through LaPlace approximation allowing for closed form calculations.This made me remember fondly some old papers of R.A.Fisher(1922).展开更多
基金Shi’s research was supported in part by the National Library of Medicine Institutional Training Grant T15 LM009451Hannig’s research was supported in part by the National Sci-ence Foundation(NSF)under Grant Nos.1512945,1633074,and 1916115Lee’s research was supported in part by the NSF under Grant No.1512945 and 1513484.
文摘As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for decades.Much work has been done under the frequentist and Bayesian frameworks.Aiming to quantify the uncertainty of the estimators without having to choose a prior,we have developed a fiducial approach to the estimation of covariance matrix.Built upon the Fiducial Berstein-von Mises Theorem,we show that the fiducial distribution of the covariate matrix is consistent under our framework.Consequently,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 matrix.Lastly,we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.
基金supported by National Natural Science Foundation of China(Grant No.U23A2064)Singapore Ministry of Education+1 种基金U.S.National Institute of HealthU.S.National Science Foundation。
文摘Fiducial inference is applied to nonparametric g-modeling in the discrete case.We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals.We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios.The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals.Furthermore,we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients.
基金This work was supported by the China Scholarship Council[Grant Number 201906140047]National Natural Science Foundation of China[Grant Numbers 11801210,11801359 and 11771145].
文摘In this paper,we propose generalized fiducial methods and construct four generalized p-values to test the existence of quantitative trait locus effects under phenotype distributions from a location-scale family.Compared with the likelihood ratio test based on simulation studies,our methods perform better at controlling type I errors while retaining comparable power in cases with small or moderate sample sizes.The four generalized fiducial methods support varied sce-narios:two of them are more aggressive and powerful,whereas the other two appear more conservative and robust.A real data example involving mouse blood pressure is used to illustrate our proposed methods.
文摘In this study,the authors proposed upper tolerance limits for the gamma mixture distribution based on generalized fiducial inference,and an MCMC simulation is performed to sample from the generalized fiducial distributions.The simulation results and a real hydrological data example show that the proposed tolerance limits are more efficient.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10771015 and the Start-Up Funds for Doctoral Scientific Research of Shandong University of Finance.
文摘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.
基金Jan Hannig’s research was supported in part by the National Science Foundation[grant number 1512945 and 1633074].
文摘The authors should be congratulated on a stimulating piece of work.There is definitely a great need to understand information-based criteria such as BIC better.I especially especially enjoyed the way they simplified the problem through LaPlace approximation allowing for closed form calculations.This made me remember fondly some old papers of R.A.Fisher(1922).
