On Optimal and Asymptotic Properties of a Fuzzy L 2 Estimator

Jin Hee Yoon and Przemyslaw Grzegorzewski
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Jin Hee Yoon: Department of Mathematics and Statistics, Sejong University, Seoul 05006, Korea
Przemyslaw Grzegorzewski: Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Wasaw, Poland

Mathematics, 2020, vol. 8, issue 11, 1-16

Abstract: A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L 2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

Keywords: fuzzy random variable; fuzzy least squares estimator; triangular fuzzy matrix; fuzzy-type linear estimator; unbiased estimator; BLUE; consistency; asymptotic normality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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