| In the science of surveying and mapping, people researched and discussed the systematic errors or gross errors on one or a few observations in the past, the reasons are that static ground observations are less impacted by outside surrounding environment factors as the static surveying to be accomplished with conventional instruments and methods. Through duplicate experiments impacting factors (usually called systematic errors or outliers) that influence result of observation are much known, and systematic errors can be fairly compensated or be expressed in parameter model before adjustment. Furthermore observation quantity is less, and there are fairly perfect observation procedures and checking conditions (such as definite geometric conditions), so outliers are easily detected or cleared up. It can reach up to be ignored comparing remainder system errors with occasional errors. Though there is individual error, many methods (data snooping, robust estimate etc.) can deal with it. along with development of surveying instruments and technologies, especially extensive application of space technologies, a great deal of surveying data can be gained in the short time, moreover, data is seriously influenced by outside environment, and factors impacting observation results is too much , and its function relation is complicated and unknown. If not considering this the parametric model is approximately built, and it can bring forward not ignored deviation between parametric model and real model, and seriously influenced estimates. In a sense, the classical parametric regression model does not solve essentially model error, and also can not fundamentally distinguish system errors with gross errors, or mix up both. When the adjustment model include systematic errors and outliers, the method dealing with model errors is not quite satisfactory , so it is necessary that the new data processing methods to improve present theories of surveying data processing.From what has been discussed above, researching and resolving model errors, or differentiating systematic error with gross is one of the main contents to be researched nowadays.The eighth decade of the 20th century, a important statistical model ——the semiparametricregression model has been developed, it is a fire-new method for us to research the above problems.The semiparametric model is as follows:L=BX+s(t)+△Where s(t) is the model errors (here called function model errors) describing unknown function relation, and it is the function of variablet, and is called the non-parameter. It can overcome the demerits of conventional adjustment model and get mathematics model close to reality since the non-parametric weight be brought in the semiparametric model. The parameter, non-parameter and accidental error can be got if an estimation method is used, and it will be an ideal method, moreover has very good foreground of application. Duo to these reasons above the semiparametric model is given abroad attentions, and the writer deal with model errors mainly in surveying data modeling with its theories and methods, and research model diagnose and gross test etc. At the same time, surveying data processing be combined with surveying practice to solve practical questions.The paper is divided into seven chapters. In chapter one, introduction expatiate the present stateof research on the model errors and the semiparametric model estimation, and clarify content and signification. The main contents are as follows on the other chapters:In chapter 2, it clarifies the basic theories and methods on the data processing of linear parameter model, Including parameter estimation, test of parameter significance, model diagnose and outlier test. It give methods of residual analysis and test, and bring forward questions to be solved: 1 .. how do you deal with it when there is systematical errors in adjustment model ? 2, how do you snoop outliers and estimate systematical errors when both is at one time?In chapter 3, especially researching estimation methods of the semi-parametric mode based on regular matrix; detailedly deriving the penalized least square formulas of the nonparametric model with natural spline, and giving the penalized least square formulas of the semiparametric model with cubic natural spline; in addition, introducing partial kernel smoothing and partial residual estimate. Giving penalized least square formulas of the semi-parametric model with vector measurements. The choices of regular matrix and smoothing factor are systematically discussed, finally giving some statistical properties for the estimates of the semiparametric model.In chapter 4, based on the diagnose means of parametric model, testifying the estimates are identical using forecasted and deleted models to estimate parameters in the semi-parametric model. Some statistical diagnose are derived and testing methods on gross errors are given. Discussing method on the test of non-parameter significance and giving its testing formulas, and finally it give brief processes and steps in the modeling of generalized linear models.In chapter 5, by analysis and comparison of several adjustment models (such as rank-deficient free network, least square collocation, ridge estimate, semi-parametric model). Putting forward the unified principle of their solutions to be derived and the unified formula of solutions on ill-posed problems. The characters of solution on ridge estimate of ill-posed problems are systematically expounded. Along with basic principle of ridge estimate of parameter, the rule of universal penalized least squares is represented based on penalized least squares of the semi-parametric model, and its formula of estimate are derived. In addition, summing up the basic theories and methods of M-estimation, and the principle of parametric robust estimate is applied on estimate of the semi-parametric model, and robust estimate of the semi-parametric model is put forward, some expressions of estimations are got for robust penalized least squares and robust universal penalized least squares. Finally simulation examples are used to illustrate the effect of related estimation methods.In chapter 6, it is combined with some examples in survey, and researched on the applications of the semi-parametric model on surveying data processing. It verifies the practicality and effect of semiparametric model with computing and analyzing of some examples.In the end, the main research work and innovation in the paper are summarized, and some problems to be further studied in the future are bring forward.
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