Abstract
Most of the conventional regression methods can only estimate a piecewise polynomial function in which the exact positions or the probabilistic distribution of the change-points is prespecified. This paper proposes an optimization method to estimate a piecewise polynomial function with unknown change-points. We first express a piecewise function by the addition of some absolute terms. Utilizing the properties of this function, a piecewise regression model is then formulated to minimize the estimation errors subjected to an amount of change-points. The model is then solved by a modified goal programming technique, which is more computationally efficient than conventional goal programs. Numerical examples demonstrate that the proposed method is very promising in estimating the piecewise regression with automatic change-point detection.
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