Skewness-kurtosis adjusted confidence estimators and significance tests

Wolf-Dieter Richter ()
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Wolf-Dieter Richter: University of Rostock

Journal of Statistical Distributions and Applications, 2016, vol. 3, issue 1, 1-8

Abstract: Abstract 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. A limit theorem for large deviations by S.V. Nagajev/V.V. Petrov applies to prove the results. Applications are given for exponential families.

Keywords: Orders of confidence; Orders of modified local alternatives; True non-covering probabilities; Local non-true parameter choice; Covering probabilities; Linnik condition; Osipov-type condition; Skewness-kurtosis adjusted decisions; Order of significance; Error probabilities of first and second kind; Exponential family; Large deviations; 62E20; 62F05; 62F12; 60F10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1186/s40488-016-0042-3

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