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Statistical Methods for Fuzzy Data by Reinhard Viertl

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22.1 Fuzzy estimators of regression parameters

Based on the fuzzy a posteriori density π*(·|z*) on the parameter space Θ ⊆r generalized point estimators for the parameter θ = (θ1,…,θr) can be calculated.

Without any loss function the most popular method is to calculate the generalized expectation of j with respect to π*(·|z*); i.e.

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where πj*(·|z*) is the fuzzy marginal density

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The characterizing function ψj(·) of j* is obtained via the construction lemma for characterizing functions. The nested family of subsets of is given by

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where

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and

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Then ψj(·) of j* is given by its values

Another possibility ...

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