NDLI: A multiple linear regression model for imprecise information

Content Provider	Springer Nature Link
Author	Ferraro, Maria Brigida Giordani, Paolo
Copyright Year	2011
Abstract	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 LR family (LR 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 LR 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.
Starting Page	1049
Ending Page	1068
Page Count	20
File Format	PDF
ISSN	00261335
Journal	Metrika
Volume Number	75
Issue Number	8
e-ISSN	1435926X
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-07-23
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	LR fuzzy data Regression models Least squares approach Bootstrap procedure Statistics Economic Theory Statistics for Business/Economics/Mathematical Finance/Insurance Probability Theory and Stochastic Processes
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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