Random Sets and Exact Confidence Regions
Ryan Martin
- Vol. 76, Iss: 2, pp 288-304
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TLDR
This paper describes a new approach, using random sets, which allows users to construct exact confidence regions without appeal to asymptotic theory, if the user-specified random set satisfies a certain validity property.Abstract:
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold approximately, for large samples. This paper describes a new approach, using random sets, which allows users to construct exact confidence regions without appeal to asymptotic theory. In particular, if the user-specified random set satisfies a certain validity property, confidence regions obtained by thresholding the induced data-dependent plausibility function are shown to have the desired coverage probability.read more
Citations
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Journal ArticleDOI
Plausibility Functions and Exact Frequentist Inference
TL;DR: In this article, a general framework for the construction of exact frequentist procedures based on plausibility functions is presented, and it is shown that the plausibility function-based tests and confidence regions have the desired frequentist properties in finite samples.
Journal ArticleDOI
A note on p-values interpreted as plausibilities
Ryan Martin,Chuanhai Liu +1 more
TL;DR: It is shown that, for most practical hypothesis testing problems, there exists an inferential model such that the corresponding plausibility function, evaluated at the null hypothesis, is exactly the p-value.
Journal ArticleDOI
Inferential models: A framework for prior-free posterior probabilistic inference
Ryan Martin,Chuanhai Liu +1 more
TL;DR: In this paper, the authors present a new framework for probabilistic inference based on inferential models (IMs), which not only provides data-dependent measures of uncertainty about the unknown parameter, but does so with an automatic long-run frequency calibration property.
Journal ArticleDOI
Prior-Free Probabilistic Prediction of Future Observations
Ryan Martin,Rama T. Lingham +1 more
TL;DR: An IM-based technique is employed to marginalize out the unknown parameters, yielding prior-free probabilistic prediction of future observables, which is expected to be a useful tool for practitioners.
Journal ArticleDOI
Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model
TL;DR: The authors proposed a new inferential model approach which yields exact prior-free probabilistic inference on the heritability coefficient, and constructed exact confidence intervals and demonstrate numerically their method's efficiency compared to that of existing methods.
References
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An introduction to the bootstrap
Bradley Efron,Robert Tibshirani +1 more
TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
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TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
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Upper and Lower Probabilities Induced by a Multivalued Mapping
TL;DR: A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
Upper and Lower Probabilities Induced by a Multivalued Mapping.
TL;DR: In this paper, a multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over S. Some basic properties of such systems are explored in Sects. 1 and 2.
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