Confidence intervals for the parameters of a linear regression model with a fuzzy response variable and a set of real and/or fuzzy explanatory variables are investigated. The family of LR fuzzy random variables is considered and an appropriate metric is suggested for coping with this type of variables. A class of linear regression models is then proposed for the center and for suitable transformations of the spreads in order to satisfy the non-negativity conditions for the latter ones. Confidence intervals for the regression parameters are introduced and discussed. Since there are no suitable parametric sampling models for the imprecise variables, a bootstrap approach has been used. The empirical behavior of the procedure is analyzed by means of simulated data and a real-case study. © Springer-Verlag 2013.
Bootstrap confidence intervals for the parameters of a linear regression model with fuzzy random variables / Ferraro, MARIA BRIGIDA; Coppi, Renato; Gil Gonzalez, Rodriguez. - 285(2013), pp. 33-42. - STUDIES IN FUZZINESS AND SOFT COMPUTING. [10.1007/978-3-642-30278-7_3].
Bootstrap confidence intervals for the parameters of a linear regression model with fuzzy random variables
FERRARO, MARIA BRIGIDA;COPPI, Renato;
2013
Abstract
Confidence intervals for the parameters of a linear regression model with a fuzzy response variable and a set of real and/or fuzzy explanatory variables are investigated. The family of LR fuzzy random variables is considered and an appropriate metric is suggested for coping with this type of variables. A class of linear regression models is then proposed for the center and for suitable transformations of the spreads in order to satisfy the non-negativity conditions for the latter ones. Confidence intervals for the regression parameters are introduced and discussed. Since there are no suitable parametric sampling models for the imprecise variables, a bootstrap approach has been used. The empirical behavior of the procedure is analyzed by means of simulated data and a real-case study. © Springer-Verlag 2013.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
