S.G. Meintanis , B. Milošević , M.D. Jiménez–Gamero
{"title":"基于最小特征函数的拟合优度检验","authors":"S.G. Meintanis , B. Milošević , M.D. Jiménez–Gamero","doi":"10.1016/j.csda.2024.107988","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>–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.</p></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167947324000720/pdfft?md5=345ca757392dc6a128ee30fc0f6964c2&pid=1-s2.0-S0167947324000720-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Goodness–of–fit tests based on the min–characteristic function\",\"authors\":\"S.G. Meintanis , B. Milošević , M.D. Jiménez–Gamero\",\"doi\":\"10.1016/j.csda.2024.107988\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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 <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>–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.</p></div>\",\"PeriodicalId\":55225,\"journal\":{\"name\":\"Computational Statistics & Data Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0167947324000720/pdfft?md5=345ca757392dc6a128ee30fc0f6964c2&pid=1-s2.0-S0167947324000720-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Statistics & Data Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167947324000720\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Statistics & Data Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167947324000720","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Goodness–of–fit tests based on the min–characteristic function
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 –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.
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.
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III) Special Applications - [...]
IV) Annals of Statistical Data Science [...]
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