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Proceedings Paper

Proving nonsingularity of coefficient matrix in least squares normal equation of non-linear semiparametric model
Author(s): Songlin Zhang; Xiaohua Tong; Xinzhou Wang
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Paper Abstract

Non-linear Semiparametric model is a statistical model consisting of both parametric and nonparametric components, and the form of the parametric part is non-linear. The efficiency problem for a semiparametric model has been widely studied presently. Since non-linear parametric models have been studied deeply, and a set of basic theory have been set up, such as the measurement of the non-linearity of non-linear models and the statistics property of non-linear parametric estimation. Based on the nearest neighbor estimating theory of non-linear semiparametric models under the least squares principle, this paper proved the nonsingularity of coefficient matrix of normal equation under certain conditions. The nonsingularity of coefficient matrix of normal equation in least squares estimator of non-linear semiparametric models can be expanded to other least squares estimator of non-linear semiparametric models.

Paper Details

Date Published: 26 July 2007
PDF: 9 pages
Proc. SPIE 6753, Geoinformatics 2007: Geospatial Information Science, 67531N (26 July 2007); doi: 10.1117/12.761880
Show Author Affiliations
Songlin Zhang, Tongji Univ. (China)
Xiaohua Tong, Tongji Univ. (China)
Xinzhou Wang, Wuhan Univ. (China)

Published in SPIE Proceedings Vol. 6753:
Geoinformatics 2007: Geospatial Information Science
Jingming Chen; Yingxia Pu, Editor(s)

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