Asymptotic properties of least squares estimation with fuzzy observations

Authors:
Hae Kyung Kim;Jin Hee Yoon;Ying Li
Affiliations:
Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea;Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea;Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea
Venue:
Information Sciences: an International Journal
Year:
2008

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Abstract

This paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input-output and random error terms. The asymptotic normality and strong consistency of the fuzzy least squares estimator (FLSE) are investigated; a confidence region based on a class of FLSEs is proposed; the asymptotic relative efficiency of FLSEs with respect to the crisp least squares estimators is also provided and a numerical example is given. Some simulation results are also presented to illustrate the behavior of FLSEs.