Generalized Fiducial Inference: A Review and New Results

Hannig, Jan; Iyer, Hari; Lai, Randy C. S.; Lee, Thomas C.

doi:10.1080/01621459.2016.1165102

Cited by 178 publications

(207 citation statements)

References 83 publications

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“…Shemyakin, ) Bayesian posteriors plotted in Figure (b), which are indistinguishable. The two‐sided 95% fiducial interval, (98.49,105.92), reported in Hannig et al (), agrees with the IM plausibility interval obtained by using the “default” random set Eq. () in the P‐step, which we argued may not be appropriate.…”

Section: Inferential Models For a Class Of Non‐regular Modelssupporting

confidence: 84%

“…The conclusions reached by using other non‐standard approaches, such as generalized fiducial (e.g. Hannig, ; Hannig et al, ) and inferential models (Martin and Liu, ), would also be very similar to the likelihood and Bayesian conclusions in these regular problems. However, outside the class of regular models, it is less clear that all the available methods will perform similarly.…”

Section: Introductionmentioning

confidence: 78%

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Exact prior‐free probabilistic inference in a class of non‐regular models

Martin

Lin

2016

Stat

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The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends on the parameter, these asymptotic properties may be difficult to assess. Recently, an inferential model (IM) framework has been developed that provides valid prior-free probabilistic inference without the need for asymptotic justification. In this paper, we construct an IM for a class of highly non-regular models with parameter-dependent support. This construction requires conditioning, which is facilitated through the solution of a particular differential equation. We prove that the plausibility intervals derived from this IM are exact confidence intervals, and we demonstrate their efficiency in a simulation study.

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Section: Inferential Models For a Class Of Non‐regular Modelssupporting

confidence: 84%

Section: Introductionmentioning

confidence: 78%

Exact prior‐free probabilistic inference in a class of non‐regular models

Martin

Lin

2016

Stat

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“…This leads to a class of models where the fiducial is unique and determined by the sampling distribution of the data as stated in Theorem 1. The generalization in this class of models is consistent with more general definitions of a fiducial model as considered by Taraldsen and Lindqvist (2013) and Hannig et al (2016).…”

Section: Introductionsupporting

confidence: 84%

Conditional fiducial models

Taraldsen

Lindqvist

2018

Journal of Statistical Planning and Inference

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The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The arguments lead to a generalization of the classical formula found by Fisher (1930). The restricted class includes cases with discrete distributions, the case of the shape parameter in the Gamma distribution, and also the case of the correlation coefficient in a bivariate Gaussian model. One of the examples can also be used in a pedagogical context to demonstrate possible difficulties with likelihood-, Bayesian-, and bootstrap-inference. Examples that demonstrate non-uniqueness are also presented. It is explained that they can be seen as cases with restrictions on the parameter space. Motivated by this the concept of a conditional fiducial model is introduced. This class of models includes the common case of iid samples from a one-parameter model investigated by Hannig (2013), the structural group models investigated by Fraser (1968), and also certain models discussed by Fisher (1973) in his final writing on the subject.

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“…These p-values also benefit from higher-order correctness. Collecting them for different values of θ 0 yields the so-called confidence curve CV * (θ) := 2 min{H * S (θ), 1 − H * S (θ)}, introduced by Birnbaum (1961) (see Xie and Singh (2013) and Hannig et al (2016) for illustrations). We can view that graphical tool as a piled-up form of two-sided CI of equal tails at all levels.…”

Section: Theorymentioning

confidence: 99%

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

2019

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We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which the method is valid. We show the asymptotic refinements of the proposed procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for Generalized Empirical Likelihood estimation. As a by-product, our fast bootstrap provides higher-order correct asymptotic confidence distributions. Monte Carlo simulations on an autoregressive conditional duration model provide numerical evidence that the novel bootstrap yields higher-order accurate confidence intervals. A real-data application on dynamics of trading volume of stocks illustrates the advantage of our method over the routinely-applied first-order asymptotic theory, when the underlying distribution of the test statistic is skewed or fat-tailed.JEL classification: C12, C15, C22, C52, C58, G12.

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Generalized Fiducial Inference: A Review and New Results

Cited by 178 publications

References 83 publications

Exact prior‐free probabilistic inference in a class of non‐regular models

Exact prior‐free probabilistic inference in a class of non‐regular models

Conditional fiducial models

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

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