Skewness-kurtosis adjusted confidence estimators and significance tests
详细信息 查看全文
- 作者：Wolf-Dieter Richter
- 关键词：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
- 刊名：Journal of Statistical Distributions and Applications
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：3
- 期：1
- 全文大小：420 KB
- 刊物类别：Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Science, general;
- 刊物主题：Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Science, general;
- 出版者：Springer Berlin Heidelberg
- ISSN：2195-5832
文摘
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.