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A determination coefficient for a linear regression model with imprecise response

2010; Wiley; Volume: 22; Issue: 4 Linguagem: Inglês

10.1002/env.1056

1180-4009

Maria Brigida Ferraro, Ana Colubi, Gil González–Rodríguez, Renato Coppi,

Fuzzy Logic and Control Systems

EnvironmetricsVolume 22, Issue 4 p. 516-529 Research Article A determination coefficient for a linear regression model with imprecise response Maria Brigida Ferraro, Corresponding Author Maria Brigida Ferraro [email protected] Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, ItalyDipartimento di Statistica, Probabilità e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, Italy.Search for more papers by this authorAna Colubi, Ana Colubi Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Calle Calvo Sotelo S/N 33007, Oviedo, Asturias, SpainSearch for more papers by this authorGil González-Rodríguez, Gil González-Rodríguez European Centre for Soft Computing, Edificio Científico-Tecnológico, Calle Gonzalo Gutiérrez Quirós S/N 33600 Mieres, Asturias, SpainSearch for more papers by this authorRenato Coppi, Renato Coppi Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, ItalySearch for more papers by this author Maria Brigida Ferraro, Corresponding Author Maria Brigida Ferraro [email protected] Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, ItalyDipartimento di Statistica, Probabilità e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, Italy.Search for more papers by this authorAna Colubi, Ana Colubi Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Calle Calvo Sotelo S/N 33007, Oviedo, Asturias, SpainSearch for more papers by this authorGil González-Rodríguez, Gil González-Rodríguez European Centre for Soft Computing, Edificio Científico-Tecnológico, Calle Gonzalo Gutiérrez Quirós S/N 33600 Mieres, Asturias, SpainSearch for more papers by this authorRenato Coppi, Renato Coppi Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Sapienza Università di Roma, Piazzale Aldo Moro 5 00185, Rome, ItalySearch for more papers by this author First published: 03 November 2010 https://doi.org/10.1002/env.1056Citations: 32Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Fuzzy sets are often used to handle the imprecision/vagueness that affects some characteristics in environmental sciences. A determination coefficient is introduced in order to quantify the degree of relationship between an imprecise response variable and a scalar explanatory predictor in a linear regression problem. An estimator of such coefficient useful to measure the goodness of fit of the model is proposed and its strong consistency is proved. Moreover, a specific linear independence testing procedure is established and both the asymptotic significance level and the power under local alternatives are established. Since the asymptotic results require large samples, a consistent bootstrap approach is developed. The empirical behavior of the suggested methods is illustrated by means of some simulations and real-life examples. Copyright © 2010 John Wiley & Sons, Ltd. 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Citing Literature Volume22, Issue4June 2011Pages 516-529 ReferencesRelatedInformation