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An uncertain regression model

An uncertain regression model 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Grey Systems: Theory and Application Emerald Publishing

An uncertain regression model

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
2043-9377
DOI
10.1108/20439371111181215
Publisher site
See Article on Publisher Site

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.

Journal

Grey Systems: Theory and ApplicationEmerald Publishing

Published: Oct 20, 2011

Keywords: Regression analysis; Modelling; Uncertainty management; Weighted regression model; Uncertain measure; Uncertainty variable; Uncertainty multivariate distribution; Uncertain covariance; Uncertain canonical process; Intrinsic uncertain auto‐covariance matrix

References