## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

20.2 Generalized estimators for linear regression models based on the extension principle

Depending on the kind of available data generalized estimators for the parameters can be obtained in the following way:

ad (a): Yx = θ0 + θ1x1 +…+ θkxk fuzzy dependent variables yi*:

For data (x1i,…,xki; yi*), i = 1(1)n the fuzzy values yi* are characterized by their characterizing functions ηi(·), i = 1(1)n.

In this situation the estimators j for θj, j = 1(1)k can be generalized in the following way:

In order to apply the extension principle first the fuzzy data y1*,…,yn* have to be combined to form a fuzzy vector y* in n.

The vector-characterizing function ζ(·,…,·) of the combined fuzzy vector y* is obtained from the characterizing functions η1(·),…,ηn(·) by application of the minimum t-norm, i.e. the values ζ(y1…, yn) are defined by

The estimators j of the regression parameters θj can now be generalized.

Using the notation xi = (xi1,…,xik) for i = 1(1)n the estimators j for θj from Theorem 19.1 ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required