11.1 Estimators based on fuzzy samples
In reality frequently the observed samples are n fuzzy numbers x1*,…, xn* with corresponding characterizing functions ξ1(·),…,ξn(·). Therefore a classical estimator
becomes a function (x1*,…, xn*) of n fuzzy variables. Therefore by the extension principle (cf. Chapter ) the value (x1*,…, xn*) becomes fuzzy too. The characterizing function η(·) of the fuzzy value (x1*,…, xn*) is given by using the combined fuzzy sample * with vector characterizing function ξ : Mn → [0; 1] as explained in Section 10.3. Therefore the characterizing function of * = (x1*,…, xn*) is given by its values η(θ) for all θ ∈ Θ.
Using the notation = (x1,…, xn) ∈ Mn the values η(θ) are ...