Estimation of Continuous Piecewise Regression with Unknown Change-Points by Modified Goal Programming Method
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 s...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
1996
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| Online Access: | http://ndltd.ncl.edu.tw/handle/51600988271104680250 |
| Summary: | 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.
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