多面且平滑的多變量迴歸

Abstract

本文中我們討論兩種任意K次多面且平滑的多變量迴歸模式.在參數空間 上,我們建立的線性限制式能在相鄰兩個區域上滿足自由度j連續的條件, 並且我們可以利用"限制式最小平方估計法"來計算此多面且平滑的多變量 迴歸估計式. We purpose two types of multivariate regression model of arbitary polynomial order k. The linear restrictions on the parameter spa- ce that fulfill the degree j continuity of neighboring multivari- ate polynomials are derived and then the multivariate regression splines can be obtained by using the restricted least squares es- timator of regression parameters.