Axel Bücher, Christian Genest, Richard A Lockhart, Johanna G Nešlehová
{"title":"由b样条构造的Pickands依赖函数的内禀秩估计量的渐近性。","authors":"Axel Bücher, Christian Genest, Richard A Lockhart, Johanna G Nešlehová","doi":"10.1007/s10687-022-00451-9","DOIUrl":null,"url":null,"abstract":"<p><p>A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order <math><mrow><mi>m</mi> <mo>≥</mo> <mn>3</mn></mrow> </math> of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"26 1","pages":"101-138"},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9898389/pdf/","citationCount":"1","resultStr":"{\"title\":\"Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines.\",\"authors\":\"Axel Bücher, Christian Genest, Richard A Lockhart, Johanna G Nešlehová\",\"doi\":\"10.1007/s10687-022-00451-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order <math><mrow><mi>m</mi> <mo>≥</mo> <mn>3</mn></mrow> </math> of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.</p>\",\"PeriodicalId\":49274,\"journal\":{\"name\":\"Extremes\",\"volume\":\"26 1\",\"pages\":\"101-138\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9898389/pdf/\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Extremes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10687-022-00451-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Extremes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10687-022-00451-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines.
A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.
ExtremesMATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY
CiteScore
2.20
自引率
7.70%
发文量
15
审稿时长
>12 weeks
期刊介绍:
Extremes publishes original research on all aspects of statistical extreme value theory and its applications in science, engineering, economics and other fields. Authoritative and timely reviews of theoretical advances and of extreme value methods and problems in important applied areas, including detailed case studies, are welcome and will be a regular feature. All papers are refereed. Publication will be swift: in particular electronic submission and correspondence is encouraged.
Statistical extreme value methods encompass a very wide range of problems: Extreme waves, rainfall, and floods are of basic importance in oceanography and hydrology, as are high windspeeds and extreme temperatures in meteorology and catastrophic claims in insurance. The waveforms and extremes of random loads determine lifelengths in structural safety, corrosion and metal fatigue.