臺灣博碩士論文加值系統

改變點位置偵測在逐段多項式函數是一個重要問題﹐一般均需假設改變點
分配才能找到其位置﹐之後﹐求出迴歸方程。由於這是一個棘手問題﹐所
以通常假設改變點位置為已知﹐如此便可利用最小平方法或spline
method。 本論文提出以修正後目標規劃法求解在未知改變點下之連續
逐段多項式﹐首先先 介紹本法逐段多項式表示法﹑特性;其次﹐藉由其特
性利用零壹變數控制改變點個數與修正後目標規劃法﹐以互動的方式﹐完
成能同時偵測改變點位置﹑求解迴歸方程﹐進而決定滿意的改變點個數﹔
修正後目標規劃法的應用在於能提高求解的速度﹔最後﹐以兩個範例說明
本法的使用﹐如何找到改變點﹑並與Poirier''s方法與最小平方法做比較
﹐以利凸顯其優點。

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.