{"title":"Quantitative robustness of instance ranking problems","authors":"Tino Werner","doi":"10.1007/s10463-022-00847-1","DOIUrl":null,"url":null,"abstract":"<div><p>Instance ranking problems intend to recover the ordering of the instances in a data set with applications in scientific, social and financial contexts. In this work, we concentrate on the global robustness of parametric instance ranking problems in terms of the breakdown point which measures the fraction of samples that need to be perturbed in order to let the estimator take unreasonable values. Existing breakdown point notions do not cover ranking problems so far. We propose to define a breakdown of the estimator as a sign-reversal of all components which causes the predicted ranking to be potentially completely inverted; therefore, we call it the order-inversal breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for several different carefully distinguished ranking problems and provide least favorable outlier configurations, characterizations of the order-inversal breakdown point and sharp asymptotic upper bounds. We also compute empirical OIBDPs.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-022-00847-1.pdf","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-022-00847-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 2
Abstract
Instance ranking problems intend to recover the ordering of the instances in a data set with applications in scientific, social and financial contexts. In this work, we concentrate on the global robustness of parametric instance ranking problems in terms of the breakdown point which measures the fraction of samples that need to be perturbed in order to let the estimator take unreasonable values. Existing breakdown point notions do not cover ranking problems so far. We propose to define a breakdown of the estimator as a sign-reversal of all components which causes the predicted ranking to be potentially completely inverted; therefore, we call it the order-inversal breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for several different carefully distinguished ranking problems and provide least favorable outlier configurations, characterizations of the order-inversal breakdown point and sharp asymptotic upper bounds. We also compute empirical OIBDPs.
期刊介绍：
Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
