Abstract: Most data of which a statistician comes into contact has been rounded off in some manner, i.e., we do not observe X = x but a < X ≤ b. In this paper we investigate theoretical properties of the generalized fiducial distribution introduced in Hannig (2009) for such discretized data. Results are provided for both fixed sample size with increasing precision, and increasing sample size wi...

R. A. Fisher’s fiducial inference has been the subject of many discussions and controversies ever since he introduced the idea during the 1930’s. The idea experienced a bumpy ride, to say the least, during its early years and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears to have made a resurgence recently under the label of generali...

R. A. Fisher, the father of modern statistics, proposed the idea of fiducial inference during the first half of the 20th century. While his proposal led to interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher’s approach as it became apparent that some of Fisher’s bold claims about the properties of fiducial distribution did not hold up...

Abstract: In addition to the usual sources of error that have been long studied by statisticians, many data sets have been rounded off in some manner, either by the measuring device or storage on a computer. In this paper we investigate theoretical properties of generalized fiducial distribution introduced in Hannig (2009) for discretized data. Limit theorems are provided for both fixed sample ...

I consider the time evolution of generalized coherent states based on nonstandard fiducial vectors, and show that only for a restricted class of fiducial vectors does the associated classical motion determine the quantum evolution of the states. I discuss some consequences of this for path integral representations. PACS numbers: 03.65.Ca, 03.65.Bz Typeset using REVTEX 1

We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity GPQ and generalized P value GPV for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators MREs , and thus, it is an extension of the methods based onmaximum likelihood estimator...

In this article, we propose a simple method of constructing confidence intervals for a function of binomial success probabilities and for a function of Poisson means. The method involves finding an approximate fiducial quantity (FQ) for the parameters of interest. A FQ for a function of several parameters can be obtained by substitution. For the binomial case, the fiducial approach is illustrat...