On the variance of fuzzy random variables
Fuzzy Sets and Systems
Fuzzy set-theoretic methods in statistics
Fuzzy sets in decision analysis, operations research and statistics
Limit theorems for fuzzy-random variables
Fuzzy Sets and Systems
Some complete metrics on spaces of fuzzy subsets
Fuzzy Sets and Systems - Fuzzy intervals
Limit distributions of least squares estimators in linear regression models with vague concepts
Journal of Multivariate Analysis
Estimation of a simple linear regression model for fuzzy random variables
Fuzzy Sets and Systems
The fuzzy approach to statistical analysis
Computational Statistics & Data Analysis
Tools for fuzzy random variables: Embeddings and measurabilities
Computational Statistics & Data Analysis
Three-way analysis of imprecise data
Journal of Multivariate Analysis
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Linear regression models with vague concepts extend the classical single equation linear regression models by admitting observations in form of fuzzy subsets instead of real numbers. They have recently been introduced [cf. Kratschmer, Induktive statistik auf basis unscharfer meszkonzepte am beispiel linearer regressionsmodelle, Unpublished Habilitation Monograph, Faculty of Law and Economics of the University of Saarland, Saarbrucken, 2001] to improve the empirical meaningfulness of the relationship between the involved items by a more sensitive attention to the problems of data measurement, in particular the fundamental problem of adequacy. The parameters of such models are still real numbers, and a method of estimation can be applied which extends directly the ordinary least-squares method. This paper deals with some first asymptotic properties of estimators obtained by the method. Firstly, strong consistency will be shown, and secondly, the convergence rate will be investigated. The later result will be the starting point for a future study which will calculate the limit distributions of the estimators. he starting point for a future study which will calculate the limit distributions of the estimators.