2015/04/10 by Richter, Wolf-Dieter
#60F10 #62C05 #62E20 #62F03 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1504.02553
First and second kind modifications of usual confidence intervals for estimating the expectation and of usual local alternative parameter choices are introduced in a way such that the asymptotic behavior of the true non-covering probabilities and the covering probabilities under the modified local non-true parameter assumption can be asymptotically exactly controlled. The orders of convergence to zero of both types of probabilities are assumed to be suitably bounded below according to an Osipov-type condition and the sample distribution is assumed to satisfy a corresponding tail condition due to Linnik. Analogous considerations are presented for the power function when testing a hypothesis concerning the expectation both under the assumption of a true hypothesis as well as under a modified local alternative. Applications are given for exponential families.