‘Some counterexamples to the theory of confidence intervals’

Abstract

I am grateful to Dr R. Traxler for pointing out that my reference to Professor Neyman's concept of ‘shortest‘ is inaccurate. The confidenoe interval I( x ) of my third example is ‘shortest‘ in the sense of Kendall & Stuart (1967, p. 114) and admissible in the sense of Joshi (1966) but is not ‘shortest‘ in the precise sense originally used; see Neyman (1967, p. 281). In writing the paper I had intended to refer to a less specific discussion of the length of confidence intervals, Neyman (1967, p. 281). This reference and the central point of my paper are unaffeoted. JOSHI, V. M. (1966). Admiasibility of confidence intervals. Ann. Math. Statist. 37, 629–38. KENDALL, M. G. & STUART, A. (1967). The Advanced Theory of Statistics, Vol. 2, 2nd edition. London: Griffin. NEYMAN, J. (1967). A Selection of Early Statistical Papers of J. Neyman. Berkeley: University of California Press.