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
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
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).
