{"title":"Strong convergence of a nonparametric relative error regression estimator under missing data with functional predictors","authors":"Adel Boucetta, Zohra Guessoum, Elias Ould-Said","doi":"10.1007/s42952-024-00275-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we develop a nonparametric estimator of the regression function for a functional explanatory variable and a scalar response variable that is subject to left truncation and right censoring. The estimator is constructed by minimizing the mean squared relative error, which is a robust criterion that reduces the impact of outliers relatively to the Nadaraya Watson estimator. We prove the pointwise and uniform convergence of the estimator under some regular conditions and assess its performance by a numerical study. We also investigate the robustness of the estimator using the influence function as a measure of sensitivity to outliers and apply the estimator to a real dataset.</p>","PeriodicalId":49992,"journal":{"name":"Journal of the Korean Statistical Society","volume":"93 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Statistical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-024-00275-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we develop a nonparametric estimator of the regression function for a functional explanatory variable and a scalar response variable that is subject to left truncation and right censoring. The estimator is constructed by minimizing the mean squared relative error, which is a robust criterion that reduces the impact of outliers relatively to the Nadaraya Watson estimator. We prove the pointwise and uniform convergence of the estimator under some regular conditions and assess its performance by a numerical study. We also investigate the robustness of the estimator using the influence function as a measure of sensitivity to outliers and apply the estimator to a real dataset.
期刊介绍:
The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.