Confidence Distributions
摘要
A Confidence Distribution ( CD), H( X, θ), for a parameter is a function of the data, X, and the parameter in question, θ, such that: (a) for each data value X, H( X, .) is a (continuous) cumulative distribution function for the parameter, and (b) for the true parameter value, θ 0, H(., θ 0) has a uniform distribution on the interval (0,1). The concept of CD has its historic roots in Fisher’s fiducial distribution, although, in its modern version, it is a strictly frequentist construct (Schweder and Hjort, Scand. J. Statist. 29:309–332, 2002; Schweder and Hjort, Frequentist analogues of priors and posteriors. In: Econometrics and the Philosophy of Economics, pp. 285–317. Princeton University Press, Princeton, 2003; Singh et al., Ann Statist 33:159–183, 2005; Singh et al., Confidence Distribution ( CD)-distribution estimator of a parameter. In: Complex Datasets and Inverse Problems, Liu, R., Strawderman, W., Zhang, C.-H. (eds.). IMS Lecture Notes-Monograph Series, No 54, pp. 132–150, 2007, and see also Efron, Biometrika 80:3–26, 1993). The CD carries a great deal of information pertinent to a variety of frequentist inferences and may be used for the construction of confidence intervals, tests of hypotheses and point estimation.