Discussion of ‘Nonparametric generalized fiducial inference for survival functions under censoring’

Taraldsen, Gunnar; Lindqvist, Bo Henry

doi:10.1093/biomet/asz027

Cited by 6 publications

(3 citation statements)

References 6 publications

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“…Schweder and Hjort (2016) present recent developments in the theory of confidence distributions and advocates this as an alternative to the calculation of Bayesian posteriors. Taraldsen and Lindqvist (2019) explain that the problem of choosing a prior, including non-parametric problems, can be solved by not choosing a prior, but rather using the information contained in a data generating equation. Xie and Singh (2013) explain how the concept of a confidence distribution can be seen as the frequentist distribution estimator of a parameter.…”

Section: Discussionmentioning

confidence: 99%

The Confidence Density for Correlation

Taraldsen

2021

Sankhya A

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Inference 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.

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Section: Discussionmentioning

confidence: 99%

The Confidence Density for Correlation

Taraldsen

2021

Sankhya A

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“…Fiducial inference, as formulated mathematically by Taraldsen and Lindqvist (2013, 2019), and Taraldsen (2021a, is inference where a given data generating model is part of the problem formulation. Fiducial inference is then different from both Bayesian and frequentist inference since neither are based on the concept of a data generating model.…”

Section: A Mathematical Definitions and Theoremsmentioning

confidence: 99%

Fiducial Inference and Decision Theory

Taraldsen¹,

H.²

2021

Preprint

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The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to Bayesian analysis, but without requiring a prior. The prior information is replaced by assuming a particular data generating equation. Berger (1985) explains that Bayesian analysis and statistical decision theory are in harmony. Taraldsen and Lindqvist (2013) show that fiducial theory and statistical decision theory also play well together. The purpose of this text is to explain and exemplify this together with recent mathematical results. 1

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“…Based on these realizations, GFI was proposed and well‐defined by Hannig 35 . Until now, GFI has been successfully applied in many important statistical problems, such as variance components, 36,37 reliability assessment, 38–40 maximum mean of a multivariate normal distribution, 41 multiple comparisons, 42 extreme value estimation, 43 wavelet regression, 44 logistic regression and binary response models, 45 ultrahigh‐dimensional regression, 46 nonparametric inference, 47–50 and many others 51,52 …”

Section: Introductionmentioning

confidence: 99%

Hypothesis testing of process capability index Cpk from the perspective of generalized fiducial inference

Meng

Yang

Huang

2020

Quality & Reliability Eng

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Hypothesis testing of Cpk is an essential part for decision making on process capability. The difficulty to test the hypothesis of Cpk is the complexity of the natural estimator Ĉpk distribution even under the normal distribution. Thus, traditional methods of the hypothesis testing of Cpk based on the natural estimator Ĉpk only give the approximate test method under the normal distribution and seldom discuss the hypothesis testing under some commonly used but complex non‐normal distributions. The emerging generalized fiducial inference (GFI) in recent years is an effective method for statistical inference on complex statistics. Thus, we first propose a novel hypothesis testing method for Cpk based on generalized p‐value. For application, the mathematic expression of the proposed method for the commonly used normal distribution, Gamma distribution, Weibull distribution, and two‐parameter exponential distribution is derived in detail. Next, to study the performance of the proposed method in terms of the frequency property, the real probabilities of Type I error and Type II error are calculated through simulation. The calculated results show that the proposed method has satisfactory performance for different distributions. Finally, the implementation of the proposed method is illustrated by two real examples.

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Discussion of ‘Nonparametric generalized fiducial inference for survival functions under censoring’

Cited by 6 publications

References 6 publications

The Confidence Density for Correlation

The Confidence Density for Correlation

Fiducial Inference and Decision Theory

Hypothesis testing of process capability index Cpk from the perspective of generalized fiducial inference

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