A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy

In standard regression analysis the relationship between the (response) variable and a set of (explanatory) variables is investigated. In the classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random variable. However, the data can also be subjected to other kinds of uncertainty such as imprecision. A possible way to manage all of these uncertainties is represented by the concept of fuzzy random variable (FRV). The most common class of FRVs is the L R family (L R FRV), which allows us to express every FRV in terms of three random variables, namely, the center, the left spread and the right spread. In this work, limiting our attention to the L R FRV class, we consider the linear regression problem in the presence of one or more imprecise random elements. The procedure for estimating the model parameters and the determination coefficient are discussed and the hypothesis testing problem is addressed following a bootstrap approach. Furthermore, in order to illustrate how the proposed model works in practice, the results of a real-life example are given together with a comparison with those obtained by applying classical regression analysis.

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Fuzzy regression analysis: Systematic review and bibliography

Chukhrova

Johannssen

2019

Applied Soft Computing

101

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A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy

Cited by 5 publications

References 10 publications

An unexpected property of minimax estimation in the relative squared error approach to linear regression analysis

An unexpected property of minimax estimation in the relative squared error approach to linear regression analysis

A multiple linear regression model for imprecise information

Fuzzy regression analysis: Systematic review and bibliography

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