A determination coefficient for a linear regression model with imprecise response | Zendy

Ferraro Maria Brigida | Zendy; Colubi Ana | Zendy; GonzálezRodríguez Gil | Zendy; Coppi Renato | Zendy

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A determination coefficient for a linear regression model with imprecise response

Author(s) -

Ferraro Maria Brigida,

Colubi Ana,

GonzálezRodríguez Gil,

Coppi Renato

Publication year - 2011

Publication title -

environmetrics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.68

H-Index - 58

eISSN - 1099-095X

pISSN - 1180-4009

DOI - 10.1002/env.1056

Subject(s) - mathematics , linear regression , proper linear model , estimator , linear model , consistency (knowledge bases) , linear predictor function , statistics , vagueness , econometrics , explanatory power , independence (probability theory) , fuzzy logic , bayesian multivariate linear regression , computer science , artificial intelligence , philosophy , geometry , epistemology

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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