Semiparametric Kernel Estimation Theory And Its Application In Deformation Monitoring

So far, with the rapid development of science technology, the demands of measurement data processing become more and more increasing, but, because of the complexity of the instruments and observation data, lead to more and more data processing questions, such as some observation data are not subject to normal distribution, which resulted in failure of Least Squares; error equations or normal equations appear sick; without a clear understanding of the observations'error, so it can't be eliminated and so on. Semiparametric model contains a parametric component and a nonparametric component, which can overcome the imperfect parts of nonparametric model and parametric model, make up the shortcomings of parametric model and nonparametric model, be able to solve many practical problems. Numerous studies show that semiparametric model has many the obvious advantages, when it deals with the complex relationship between the observations and parameters to be estimated. So, it was studied and applied in many fields. Semiparametric model can deal with the system errors and gross errors, at the same time, it also can separate them, provide more reliable results for us.Semiparametric kernel estimation, includes the partial kernel smoothing estimation, the partial residual estimation, nearest neighbor kernel estimation, least squares estimation and the Nadaraya-Watson kernel estimation. Studying various theories and methods of semiparametric kernel estimation, solving the parametric component and nonparametric component of the semiparametric kernel estimation and derivation its statistical properties, find the range of this model, make it apply to the deformation monitoring and data processing, reasonable and effective deal with the system errors and gross errors, then detected and removed gross errors, improve the forecast accuracy. Therefore, this paper has a good theoretical sense and great practical value.This paper's arrangements are as follows:In the first chapter, it main discuss the research results of semiparametric model in the statistics field and Geoscience field, the adjustment model of the semiparametric and the research progress of semiparametric kernel estimation theory. About the research-based compensation for semiparametric adjustment model and the research-based predict extension of the semiparametric adjustment model, this chapter has a detailed analysis, the main difference between the two models is that the latter can change over time, more flexibility and applicability. In this paper, the semiparametric kernel estimation adjustment model is the latter.In the second chapter, the main contents are:Introduction kernel estimation theory, the kernel function and a variety of semiparametric kernel estimation methods, such as least squares kernel estimation, partial kernel smoothing estimation, the partial residual kernel estimation, nearest neighbor estimation and the Nadaraya-Watson kernel estimation, in this five kernel estimation methods, if the smooth matrix S is symmetric idempotent matrix and select the same circumstances, the results of the kernel estimation is the same, that is to say, X is the same, s also is the same. Based on small samples, select a different kernel function, estimation results are not the same, different kernel estimation methods have different characteristics, so identify the rang of the semiparametric kernel estimation methods, and discuss the weight issues of a variety of semiparametric kernel estimation model. Finally, simulation examples show that different kernel functions, estimation speed is different, that determine the speed of bandwidth parameters are also different.In the third chapter, it mainly derive the statistical properties of the semiparametric kernel estimator (parametric component and nonparametric component) and discuss the selection of bandwidth parameters. The statistical properties of the semiparametric kernel estimator include the expectation, deviation, variance and mean square error of semiparametric kernel estimator. Bandwidth parameter is a very important smoothing parameter, balancing the degree of its curve and smoothness, in fact, it plays the role of a penalty factor, which choice is good or bad influence the estimator nature. The smaller the bandwidth, the smaller the bias of the kernel estimation, but the variance is greater. In the selection of bandwidth parameters, discuss the minimum mean square error method, the minimum integral square error method, CV and GCV method, PI method, S method, T method and so on. Change in bandwidth, it is impossible to make the bias and variance of kernel estimation get smaller at the same. Therefore, the selection criteria of best bandwidth parameter must be balance between bias and variance of the kernel estimation, which can also be reflected in a few simulation examples of the chapter.In the fourth chapter, it mainly make the semiparametric kernel estimation theory apply to the deformation monitoring data processing, before its application to the deformation monitoring, is very little, therefore, this chapter test the effectiveness of its data processing, by use the actual GPS data, with different bandwidth parameters and different kernel estimation methods. The practice has proved that semiparametric kernel estimation can improve the accuracy of the deformation monitoring data processing, can forecast more accurately to the point of deformation, it is more practical as a data processing method.Chapter Five is the conclusion part, that is:by using kernel estimation theory, solution the parametric components and nonparametric components of the semiparametric kernel estimation, derived its statistical properties, discussed its kernel function and bandwidth parameter selection problem and the solution of the calculations, determined the range of the model, and apply the corresponding simulation examples to verify the results of each model. In addition, semiparametric kernel estimation theory is applied to the deformation monitoring data processing, can effectively estimate the system errors and detect gross errors, improve the accuracy of data processing, the deformation of points correctly predicted trends, try to avoid the occurrence of disasters. Conducting sum up this chapter, it is also pointed out the lack of this paper and outlook the application of semiparametric kernel estimation.