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In statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of all levels for a parameter of interest. Historically, it has typically been constructed by inverting the upper limits of lower sided confidence intervals of all levels, and it was also commonly associated with a fiducial〔 interpretation (fiducial distribution), although it is a purely frequentist concept.〔 A confidence distribution is not a valid probability distribution,〔 but may still be a function useful for making inferences.〔 In recent years, there has been a surge of renewed interest in confidence distributions. In the more recent developments, the concept of confidence distribution has emerged as a purely frequentist concept, without any fiducial interpretation or reasoning. Conceptually, a confidence distribution is no different from a point estimator or an interval estimator (confidence interval), but it uses a sample-dependent distribution function on the parameter space (instead of a point or an interval) to estimate the parameter of interest. A simple example of a confidence distribution, that has been broadly used in statistical practice, is a bootstrap distribution.〔 The development and interpretation of a bootstrap distribution does not involve any fiducial reasoning; the same is true for the concept of a confidence distribution. But the notion of confidence distribution is much broader than that of a bootstrap distribution. In particular, recent research suggests that it encompasses and unifies a wide range of examples, from regular parametric cases (including most examples of the classical development of Fisher's fiducial distribution) to bootstrap distributions, p-value functions,〔 normalized likelihood functions and, in some cases, Bayesian priors and Bayesian posteriors.〔 Just as a Bayesian posterior distribution contains a wealth of information for any type of Bayesian inference, a confidence distribution contains a wealth of information for constructing almost all types of frequentist inferences, including point estimates, confidence intervals and p-values, among others. Some recent developments have highlighted the promising potentials of the CD concept, as an effective inferential tool. == The history of CD concept == Neyman (1937)〔 introduced the idea of "confidence" in his seminal paper on confidence intervals which clarified the frequentist repetition property. According to Fraser,〔 the seed (idea) of confidence distribution can even be traced back to Bayes (1763)〔 and Fisher (1930).〔 Some researchers view the confidence distribution as "the Neymanian interpretation of Fishers fiducial distribution",〔 which was "furiously disputed by Fisher".〔 It is also believed that these "unproductive disputes" and Fisher's "stubborn insistence"〔 might be the reason that the concept of confidence distribution has been long misconstrued as a fiducial concept and not been fully developed under the frequentist framework.〔〔 Indeed, the confidence distribution is a purely frequentist concept with a purely frequentist interpretation, and it also has ties to Bayesian inference concepts and the fiducial arguments. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Confidence distribution」の詳細全文を読む スポンサード リンク
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