The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously.A class of new estimators,robust general shrunken estimators,are proposed by grafting the robust ...The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously.A class of new estimators,robust general shrunken estimators,are proposed by grafting the robust estimation techniques philosophy into the biased estimator,and their statistical properties are discussed.By appropriate choices of the shrinking parameter matrix,we obtain many useful and important estimators.A numerical example is used to illustrate that these new estimators can not only effectively overcome difficulty caused by multicollinearity but also resist the influence of outliers.展开更多
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
In this article,we consider the standard linear regression model with aggregated data T=A'Y。 We discuss the influence of aggregated data on fitted values at certain point,and get the upper or lower bound of the i...In this article,we consider the standard linear regression model with aggregated data T=A'Y。 We discuss the influence of aggregated data on fitted values at certain point,and get the upper or lower bound of the inluence. In addition ,we establish the relations between the fit statistic and correlation coefficient.展开更多
文摘The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously.A class of new estimators,robust general shrunken estimators,are proposed by grafting the robust estimation techniques philosophy into the biased estimator,and their statistical properties are discussed.By appropriate choices of the shrinking parameter matrix,we obtain many useful and important estimators.A numerical example is used to illustrate that these new estimators can not only effectively overcome difficulty caused by multicollinearity but also resist the influence of outliers.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
文摘In this article,we consider the standard linear regression model with aggregated data T=A'Y。 We discuss the influence of aggregated data on fitted values at certain point,and get the upper or lower bound of the inluence. In addition ,we establish the relations between the fit statistic and correlation coefficient.
