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.
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.
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