Fitting Partially Linear Models by Weighted Least Squares
作者:
DavidA. Harville,
期刊:
Technometrics
(Taylor Available online 1973)
卷期:
Volume 15,
issue 3
页码: 509-515
ISSN:0040-1706
年代: 1973
DOI:10.1080/00401706.1973.10489077
出版商: Taylor & Francis Group
关键词: Nonlinear Least Squares;Partially Linear Models;Nonlinear Estimation;Mathematical Modeling
数据来源: Taylor
摘要:
In fitting partially linear statistical models by least squares, several authors have demonstrated that, for fixed values of the nonlinear parameters, optimum values of the linear parameters can be determined analytically. Thus, the linear parameters can be eliminated by substitution. This reduction in the problem's dimension seems to greatly facilitate its solution by nonlinear least squares algorithms. In many applications, the partially linear model includes a strictly linear portion. In the present article, it is shown that for such models a considerable further reduction can be obtained in the necessary computations. Simultaneously, the earlier results are extended to a much broader class of models and to weighted least squares, and full-rank assumptions are removed. Under certain conditions that are generally satisfied in practice, the reduced model and sum of squares, considered as functions of the nonlinear parameters, have partial derivatives. Analytical expressions for these partials are obtained.
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