Goodness–of–fit tests based on the min–characteristic function

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Statistics & Data Analysis Pub Date : 2024-05-16 DOI:10.1016/j.csda.2024.107988

S.G. Meintanis , B. Milošević , M.D. Jiménez–Gamero

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Abstract

Tests of fit for classes of distributions that include the Weibull, the Pareto and the Fréchet families are proposed. The new tests employ the novel tool of the min–characteristic function and are based on an $L^{2}$ –type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data–standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. Asymptotic properties of the tests are investigated. A Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real–data sets.

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基于最小特征函数的拟合优度检验

提出了对包括魏布勒、帕累托和弗雷谢家族在内的各类分布的拟合度测试。新测试采用了新颖的最小特征函数工具，并基于该函数与应用于适当标准化数据的经验对应函数之间的 L2 型加权距离。如果使用分布参数的 MLE 进行数据标准化，那么该方法就简化为对已知参数值并设为 1 的标准族成员进行检验。对测试的渐近特性进行了研究。本文介绍了蒙特卡罗研究，其中包括新程序以及竞争对手使用三种极值分布进行规范测试的情况。新的检验还应用于一些真实数据集。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]

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