{"title":"An Uncertainty Based Approach for Dealing With Selection Bias in Non-Probability Samples","authors":"Pier Luigi Conti, Daniela Marella","doi":"10.1111/insr.12614","DOIUrl":null,"url":null,"abstract":"<p>The main issue with non-probability samples is that the standard design-based approach cannot be applied as the selection mechanism is unknown. In this paper, the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non-probability sample, is discussed. Furthermore, the effect on uncertainty due to the availability of extra-sample information is evaluated. First of all, the class of plausible distributions for the variable of interest is defined, a measure of uncertainty is introduced and its asymptotic properties are analysed. Next, a plausible estimate of the distribution of the variable of interest is constructed and its accuracy is evaluated. Finally, a simulation study is performed, and an application to a real case is provided.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 2","pages":"264-290"},"PeriodicalIF":1.9000,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12614","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Statistical Review","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/insr.12614","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The main issue with non-probability samples is that the standard design-based approach cannot be applied as the selection mechanism is unknown. In this paper, the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non-probability sample, is discussed. Furthermore, the effect on uncertainty due to the availability of extra-sample information is evaluated. First of all, the class of plausible distributions for the variable of interest is defined, a measure of uncertainty is introduced and its asymptotic properties are analysed. Next, a plausible estimate of the distribution of the variable of interest is constructed and its accuracy is evaluated. Finally, a simulation study is performed, and an application to a real case is provided.
期刊介绍：
International Statistical Review is the flagship journal of the International Statistical Institute (ISI) and of its family of Associations. It publishes papers of broad and general interest in statistics and probability. The term Review is to be interpreted broadly. The types of papers that are suitable for publication include (but are not limited to) the following: reviews/surveys of significant developments in theory, methodology, statistical computing and graphics, statistical education, and application areas; tutorials on important topics; expository papers on emerging areas of research or application; papers describing new developments and/or challenges in relevant areas; papers addressing foundational issues; papers on the history of statistics and probability; white papers on topics of importance to the profession or society; and historical assessment of seminal papers in the field and their impact.
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