抄録
As a powerful method to predict an objective variable from a set of k explanatory variables, we have multiple regression analysis using polynomial models. However, for the data having non-linear structure, this method has problems such as difficulty in the determination of the degree of polynomial, excessive large number of parameters to be estimated. So, in many cases, we assume a linear or quadratic polynomial model and try to fit a k-dimensional hyperplane or hypersurface to the given data in the (k+1)-dimensional real space Rk+1, independently of the structure of the data. For this reason, the accuracy of prediction is poor, particularly for the data having non-linear structure.
In the present paper, we propose a few models in which we take the structure of data into consideration in order to obtain estimates with higher accuracy. The proposed models perform prediction by transforming the points in Rk which are the values of the k explanatory variables to a 2-dimensional plane R2 and fitting a regression plane on R2, based on the information of higher moments of the explanatory variables.
