An uncertain regression model

In this paper, we propose an uncertain regression model with an intrinsic error structure facilitated by 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 treatments on the new regression model, we establish 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. Finally, the uncertain regression model is formulated and the estimation of the model coefficients is developed. Two examples is given for illustrating a small data regression analysis.