Proving nonsingularity of coefficient matrix in least squares normal equation of non-linear semiparametric model

Songlin Zhang; Xiaohua Tong; Xinzhou Wang

doi:10.1117/12.761880

26 July 2007 Proving nonsingularity of coefficient matrix in least squares normal equation of non-linear semiparametric model

Songlin Zhang, Xiaohua Tong, Xinzhou Wang

Author Affiliations +

Proceedings Volume 6753, Geoinformatics 2007: Geospatial Information Science; 67531N (2007) https://doi.org/10.1117/12.761880
Event: Geoinformatics 2007, 2007, Nanjing, China

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.

Citation Download Citation

Songlin Zhang, Xiaohua Tong, and Xinzhou Wang "Proving nonsingularity of coefficient matrix in least squares normal equation of non-linear semiparametric model", Proc. SPIE 6753, Geoinformatics 2007: Geospatial Information Science, 67531N (26 July 2007); https://doi.org/10.1117/12.761880

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