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An uncertain regression model

Renkuan Guo (Department of Statistical Sciences, University of Cape Town, Cape Town, South Africa)
Danni Guo (South African National Biodiversity Institute, Cape Town, South Africa)
YanHong Cui (Department of Statistical Sciences, University of Cape Town, Cape Town, South Africa)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 20 October 2011




The purpose of this paper is to propose an uncertain regression model with an intrinsic error structure facilitated by an uncertain canonical process.


This model is suitable for dealing with expert's knowledge ranging from small to medium size data of impreciseness. In order to have a rigorous mathematical treatment on the new regression model, this paper establishes a series of new uncertainty concepts sequentially, such as uncertainty joint multivariate distribution, the uncertainty distribution of uncertainty product variables and uncertain covariance and correlation based on the axiomatic uncertainty theoretical foundation. Two examples are given for illustrating a small data regression analysis.


The uncertain regression model is formulated and the estimation of the model coefficients is developed.

Practical implications

The paper is devoted to a regression model to handle a small amount of data with mathematical rigor.


The theory and the methodology of the uncertain canonical process regression is proposed for the first time. It addresses the practical challenges of small data size modelling.



Guo, R., Guo, D. and Cui, Y. (2011), "An uncertain regression model", Grey Systems: Theory and Application, Vol. 1 No. 3, pp. 202-215.



Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited

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