It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class c...Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.展开更多
Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and co...Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.展开更多
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
文摘Objectives: The objective is to analyze the interaction of the correlation structure and values of the regressor variables in the estimation of a linear model when there is a constant, possibly negative, intra-class correlation of residual errors and the group sizes are equal. Specifically: 1) How does the variance of the generalized least squares (GLS) estimator (GLSE) depend on the regressor values? 2) What is the bias in estimated variances when ordinary least squares (OLS) estimator is used? 3) In what cases are OLS and GLS equivalent. 4) How can the best linear unbiased estimator (BLUE) be constructed when the covariance matrix is singular? The purpose is to make general matrix results understandable. Results: The effects of the regressor values can be expressed in terms of the intra-class correlations of the regressors. If the intra-class correlation of residuals is large, then it is beneficial to have small intra-class correlations of the regressors, and vice versa. The algebraic presentation of GLS shows how the GLSE gives different weight to the between-group effects and the within-group effects, in what cases OLSE is equal to GLSE, and how BLUE can be constructed when the residual covariance matrix is singular. Different situations arise when the intra-class correlations of the regressors get their extreme values or intermediate values. The derivations lead to BLUE combining OLS and GLS weighting in an estimator, which can be obtained also using general matrix theory. It is indicated how the analysis can be generalized to non-equal group sizes. The analysis gives insight to models where between-group effects and within-group effects are used as separate regressors.
文摘Abstract： In this paper, we discuss the influence analysis of BLUE in growth curve model with covariate matrix disturbance, and establish the relationships of BLUEs among different models, give the measurement and computational formula which can assess the disturbing influence.
