Asymptotic and finite sample properties of Hill-type estimators in the presence of errors in observations

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2022-10-24 DOI:10.1080/10485252.2022.2136662

Mihyun Kim, P. Kokoszka

引用次数: 0

Abstract

We establish asymptotic and finite sample properties of the Hill and Harmonic Moment estimators applied to heavy-tailed data contaminated by errors. We formulate conditions on the errors and the number of upper order statistics under which these estimators continue to be asymptotically normal. We specify analogous conditions which must hold in finite samples for the confidence intervals derived from the asymptotic normal distribution to be reliable. In the large sample analysis, we specify conditions related to second-order regular variation and divergence rates for the number of upper order statistics, k, used to compute the estimators. In the finite sample analysis, we examine several data-driven methods of selecting k, and determine which of them are most suitable for confidence interval inference. The results of these investigations are applied to interarrival times of internet traffic anomalies, which are available only with a round-off error.

查看原文本刊更多论文

观测值存在误差时hill型估计量的渐近和有限样本性质

我们建立了应用于被误差污染的重尾数据的希尔矩估计和调和矩估计的渐近和有限样本性质。我们给出了这些估计量继续渐近正态的误差和上阶统计量的个数的条件。我们指定了类似的条件，这些条件必须在有限样本中成立，由渐近正态分布导出的置信区间才可靠。在大样本分析中，我们为用于计算估计量的上阶统计量k指定了与二阶正则变化和散度率相关的条件。在有限样本分析中，我们研究了几种选择k的数据驱动方法，并确定其中哪一种最适合置信区间推断。这些调查结果应用于互联网流量异常的到达间隔时间，该时间只有舍入误差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.