scholarly journals Deep fiducial inference

Stat ◽  
2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Gang Li ◽  
Jan Hannig
Keyword(s):  
Fiducial Inference

Kyburg and Fiducial Inference

1981 ◽  
Vol 48 (1) ◽  
pp. 78-91
Author(s):  
Stephen Leeds
Keyword(s):  
Fiducial Inference

scholarly journals Covariance estimation via fiducial inference

2021 ◽  
pp. 1-16
Author(s):  
W. Jenny Shi ◽  
Jan Hannig ◽  
Randy C. S. Lai ◽  
Thomas C. M. Lee
Keyword(s):  
Covariance Estimation ◽  
Fiducial Inference

scholarly journals The Confidence Density for Correlation

Sankhya A ◽  
2021 ◽  
Author(s):  
Gunnar Taraldsen
Keyword(s):  
Explicit Formula ◽  
Posterior Distribution ◽  
Hypergeometric Functions ◽  
Real Data ◽  
Numerical Calculations ◽  
Posterior Density ◽  
Fiducial Inference ◽  
Objective Prior ◽  
Confidence Distribution ◽  
New Formula

AbstractInference for correlation is central in statistics. From a Bayesian viewpoint, the final most complete outcome of inference for the correlation is the posterior distribution. An explicit formula for the posterior density for the correlation for the binormal is derived. This posterior is an optimal confidence distribution and corresponds to a standard objective prior. It coincides with the fiducial introduced by R.A. Fisher in 1930 in his first paper on fiducial inference. C.R. Rao derived an explicit elegant formula for this fiducial density, but the new formula using hypergeometric functions is better suited for numerical calculations. Several examples on real data are presented for illustration. A brief review of the connections between confidence distributions and Bayesian and fiducial inference is given in an Appendix.

scholarly journals Reply: The Functional-Model Basis of Fiducial Inference

1982 ◽  
Vol 10 (4) ◽  
pp. 1074-1074 ◽  
Author(s):  
Professor Dawid ◽  
Professor Stone
Keyword(s):  
Functional Model ◽  
Fiducial Inference

scholarly journals Fiducial Distributions in Fiducial Inference

1938 ◽  
Vol 9 (4) ◽  
pp. 272-280 ◽  
Author(s):  
S. S. Wilks
Keyword(s):  
Fiducial Inference

Fiducial Inference

2018 ◽  
pp. 4564-4567
Author(s):  
D. A. S. Fraser
Keyword(s):  
Fiducial Inference

Fiducial Inference

2011 ◽  
pp. 515-519
Author(s):  
Jan Hannig ◽  
Hari Iyer ◽  
Thomas C. M. Lee
Keyword(s):  
Fiducial Inference

scholarly journals Nonparametric generalized fiducial inference for survival functions under censoring

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 501-518 ◽  
Author(s):  
Y Cui ◽  
J Hannig
Keyword(s):  
Confidence Intervals ◽  
Average Length ◽  
Asymptotic Methods ◽  
Survival Function ◽  
Right Censoring ◽  
Rank Tests ◽  
Fiducial Inference ◽  
Fiducial Distribution ◽  
Von Mises ◽  
Log Rank Tests

Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.

Fiducial Inference

2014 ◽  
Author(s):  
Robert J. Buehler
Keyword(s):  
Fiducial Inference
Sign in / Sign up

Export Citation Format

Share Document