A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inve...A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.展开更多
The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type est...The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.展开更多
Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field o...Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field of geodetic data processing,according to the application and practice of geodesy,they have made significant contributions in the fields of hypothesis testing theory,un-modeled error,outlier detection,and robust estimation,variance component estimation,complex least squares,and ill-posed problems treatment.Many functional models such as the nonlinear adjustment model,EIV model,and mixed additive and multiplicative random error model are also constructed and improved.Geodetic data inversion is an important part of geodetic data processing,and Chinese scholars have done a lot of work in geodetic data inversion in the past five years,such as seismic slide distribution inversion,intelligent inversion algorithm,multi-source data joint inversion,water reserve change and satellite gravity inversion.This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years,analyzes the methods used by scholars and the problems solved,and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.展开更多
文摘A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.
文摘The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.
基金National Natural Science Foundation of China(No.42174011)。
文摘Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field of geodetic data processing,according to the application and practice of geodesy,they have made significant contributions in the fields of hypothesis testing theory,un-modeled error,outlier detection,and robust estimation,variance component estimation,complex least squares,and ill-posed problems treatment.Many functional models such as the nonlinear adjustment model,EIV model,and mixed additive and multiplicative random error model are also constructed and improved.Geodetic data inversion is an important part of geodetic data processing,and Chinese scholars have done a lot of work in geodetic data inversion in the past five years,such as seismic slide distribution inversion,intelligent inversion algorithm,multi-source data joint inversion,water reserve change and satellite gravity inversion.This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years,analyzes the methods used by scholars and the problems solved,and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.
