Direct estimating formulas of least squares kernel estimator of nonlinear semiparametric models

Songlin Zhang; Xiaohua Tong

doi:10.1117/12.815659

29 December 2008 Direct estimating formulas of least squares kernel estimator of nonlinear semiparametric models

Songlin Zhang, Xiaohua Tong

Proceedings Volume 7285, International Conference on Earth Observation Data Processing and Analysis (ICEODPA); 72853B (2008) https://doi.org/10.1117/12.815659
Event: International Conference on Earth Observation Data Processing and Analysis, 2008, Wuhan, China

Abstract

In some fields of space science such as GPS positioning system and remote sensing image processing, the function model is physically unambiguous and nonstatistical, and many of them are nonlinear. Further more, data collected in many fields of space science include systematic errors inevitably, parametric models sometimes are in difficulty to deal with them, and semiparametric model is an approach to solve this kind of problems. This paper focuses on a kind of semiparametric model with a nonlinear parametric component, in which the nonlinear parametric component is used to express the physical relationship and the nonparametric component is used to describe systematic errors and other model errors. The resolving of nonlinear semiparametric model is a new problem now. The most general method is linearization, but linearization is likely to introduce model error in to the model. In this paper, the direct estimating formulas of kernel method under the least-squares principle of this kind of model are deduced, including the calculating formulae of the estimation of parametric and nonparametric components, and gives the direct nonlinear estimating formulas of kernel estimator considering the second order items. Based on direct estimating formulas and simulated GPS observation data, this paper proved that: as to some least-squares kernel estimating of nonlinear semiparametric models, we can use direct estimating methods considering the second order items.

Citation Download Citation

Songlin Zhang and Xiaohua Tong "Direct estimating formulas of least squares kernel estimator of nonlinear semiparametric models", Proc. SPIE 7285, International Conference on Earth Observation Data Processing and Analysis (ICEODPA), 72853B (29 December 2008); https://doi.org/10.1117/12.815659

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KEYWORDS

Data modeling

Global Positioning System

Satellites

Error analysis

Statistical modeling

Statistical analysis

Earth observing sensors

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