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Grey Systems: Theory and Application
ISSN: 2043-9377
Online from: 2011
Subject Area: Information and Knowledge Management
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An uncertain regression model
| Title: | An uncertain regression model |
|---|---|
| Author(s): | 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) |
| Citation: | Renkuan Guo, Danni Guo, YanHong Cui, (2011) "An uncertain regression model", Grey Systems: Theory and Application, Vol. 1 Iss: 3, pp.202 - 215 |
| Keywords: | Intrinsic uncertain auto-covariance matrix, Modelling, Regression analysis, Uncertain canonical process, Uncertain covariance, Uncertain measure, Uncertainty management, Uncertainty multivariate distribution, Uncertainty variable, Weighted regression model |
| Article type: | Research paper |
| DOI: | 10.1108/20439371111181215 (Permanent URL) |
| Publisher: | Emerald Group Publishing Limited |
| Acknowledgements: | This research is supported financially by the South African National Research Foundation (IFR2011040400096) and (IFR2009090800013), and by the University of Cape Town Postgraduate Fellowship 2011. The authors would like to thank the California Air Resources Board for providing the air quality data used in this paper, also Professor B.D. Liu and his PhD students: Dr W. Dai, Dr X.W. Chen, K. Yao, and Z.X. Peng, for their invaluable debates and input. |
| Abstract: | Purpose – The purpose of this paper is to propose an uncertain regression model with an intrinsic error structure facilitated by an uncertain canonical process. Design/methodology/approach – 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. Findings – 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. Originality/value – 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. |
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