cramsamr -von- mises检验超额在一个置信水平上的分布

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2023-02-09 DOI:10.1080/10485252.2023.2173958

D. Gaigall, Julian Gerstenberg

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引用次数: 0

摘要

cramsamr -von- mises距离应用于超过置信水平的超额分布。研究了相关统计量的渐近性，得到的极限分布不同于经典的极限分布。因此，给出了新极限分布的分位数，并介绍了用于近似目的的新自举技术。这些结果激发了新的单样本拟合优度检验，用于检验超过置信水平的过剩分布，并为相关拟合误差提供了新的置信区间。模拟研究调查了测试的大小和能力，以及有限样本情况下置信区间的覆盖概率。克拉姆塞姆-冯-米塞斯测试面向实践的应用是确定拟合方法的适当置信水平。在峰值超过阈值建模的背景下，采用该思想来解决众所周知的阈值检测问题，并通过数据示例进行了概述和说明。

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Cramér-von-Mises tests for the distribution of the excess over a confidence level

The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.

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来源期刊

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics: Nonparametric modeling, Nonparametric function estimation, Rank and other robust and distribution-free procedures, Resampling methods, Lack-of-fit testing, Multivariate analysis, Inference with high-dimensional data, Dimension reduction and variable selection, Methods for errors in variables, missing, censored, and other incomplete data structures, Inference of stochastic processes, Sample surveys, Time series analysis, Longitudinal and functional data analysis, Nonparametric Bayes methods and decision procedures, Semiparametric models and procedures, Statistical methods for imaging and tomography, Statistical inverse problems, Financial statistics and econometrics, Bioinformatics and comparative genomics, Statistical algorithms and machine learning. Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order. Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.