Estimation of Continuous Piecewise Regression with Unknown Change-Points by Modified Goal Programming Method

• Main Authors: Yu, Jing-Rung, 余菁蓉
• Other Authors: Li Han-Lin
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/51600988271104680250

碩士 === 國立交通大學 === 資訊管理研究所 === 84 === An essence problem in estimating a piecewise polynomial function is the positions of change-points. Suppose the positions of the change-points are known(fixed constants), the polynomial function can then be estimated straight forward by least squares methods or spline method. This paper proposes a Least Absolute Deviations( LAD, L1-norm ) method to estimate a piecewise polynomial function with unknown change-points. We first express a piecewise polynomial function by a series of absolute terms. Utilizing the properties of this function, a goal programming model is formulated to minimize the estimation errors within a given number of change-points. The model is solved by a modified goal programming technique which is more computational efficiency than conventional goal programing methods. We show two examples in Chapter 4 to describe how the proposed method does.