Regression criteria and their application in different modeling cases
Different regression criteria exhibit different properties when used for fitting purposes. In this paper the properties of different regression criteria are described in detail. The underlying error structure and the link between the regression criterion and the application area is analysed. Examples in different modeling areas are provided. Given are an example of device modeling, system-level modeling, and the temperature decay of a biomedical sensor chip. The examples show that there does not exist an ideal regression criterion. The most appropriate regression criterion depends on the composition of the total error. If this total error has a non-Gaussian structure, the well-known least mean square criterion is not the most appropiate. This makes fitting a multiple step process. Only after some trial fittings and analysis of the resulting residual distribution, one is able to determine the most appropriate regression criterion for a given application.
regression modeling least mean squares minimax