Application Of Semi-parametric Model In Measurement Data Processing

In recent years,as an important statistical model developed in the 1980s for parameter research,semi-parametric models have been widely used in many fields.Therefore,relevant scholars introduce semi-parametric models into the data processing of measurement adjustment.When there are model errors that can not be eliminated in the observed values,the model errors can neither establish a functional relationship with the observed values nor be classified into the error items of parametric models or processed by non-parametric models.The semi-parametric model uses non-parametric vectors to represent the model errors in the adjustment model,so that the adjustment model takes into account both the characteristics of parametric models and non-parametric models.Therefore,when processing the measurement data with model errors,the semi-parametric model is closer to the actual problem in mathematical model,and can solve both model error and accidental error in numerical solution.This paper aim at the basic theory of semi-parametric model and its application in measurement data processing are mainly studied as follows:1.Aiming at the problem of model errors which can not be ignored in the observed data,introduced the basic theory of semi-parametric model.Constructing normal equation based on compensated least squares criterion to solve parameter vector and non-parametric vector,and giving the statistical hypothesis test of semi-parametric model.In the process of constructing normal equation,the selection of regular matrix and regularization parameter is the key step to obtain the optimal estimation.This paper summarizes the selection methods of regular matrix and regularization parameter,and studies the golden section method as an example to calculating the optimal regularization parameters.2.Aiming at the singular of coefficient matrix of error equation's normal equation,introduced the generalized compensated least squares estimation and ridge estimation.Since the two criteria are equivalent in the semi-parametric model,so studied the semi-parametric ridge estimation model in this paper and summarized the selection method of ridge parameters.Finally,constructed the normal equation with the generalized compensated least squares.According to in different cases of ill-conditioned coefficient matrix of normal equation,solve the parametric and non-parametric vectors of the semi-parametric model.3.Aim to solve the problem of compensated least squares estimation and semi-parametric ridge estimation are not have robust when adjustment model contains gross error,introduced robust estimation theory and discussed robust estimation of semi-parametric model.Based on the robust estimation criterion of semi-parametric model,solved the parameters and non-parametric estimates of semi-parametric model robust estimation.At the same time,considering the influence of initial residuals on the iterative process of robust estilmation,established a joint robust model of 1-norm minimization method and robust estimation,summarized the semi-parametric robust estimation model's iterative flow.4.Aim to the theory of semi-parametric model,this paper uses simulation data and measured data to verify the effectiveness and superiority of semi-parametric model in solving data processing problems.Designed different calculation schemes in simulated data calculated parameter problems and set the semi-parametric grey Verhulst model of the surface subsidence in mining area.The experimental results show that the accuracy of parameter estimation of semi-parametric model is better than that of parametric model when the model error can not be neglected.