The problem of consistent estimation of the regression coefficients when some prior information about the regression coefficients is available is considered. Such prior information is expressed in the form of exact linear restrictions. The knowledge of covariance matrix of measurement errors that is associated with explanatory variables is used to construct… (More)
The coefficient of determination (R 2) is used for judging the goodness of fit in a linear regression model. It gives valid results only when the observations are correctly observed without any measurement error. The R 2 provides invalid results in the presence of measurement errors in the data in the sense that sample R 2 becomes an inconsistent estimator… (More)
AMS (2010) subject classifications: 62J05 62H12 Keywords: Coefficient of determination Goodness of fit Least squares estimator Linear equality constraint Measurement error Restricted regression Ultrastructural model a b s t r a c t The restricted measurement error model is employed when certain study variables are not observable by direct measurement and if… (More)
AMS subject classifications: 62J05 Keywords: Linear regression model Simultaneous forecasting Least squares estimator Stein-rule estimator Small disturbance asymptotic theory Minimum risk approach a b s t r a c t This paper deals with the improved forecasts for the values of the study variable in linear regression models utilizing the minimum risk approach.… (More)
The risk of the family of feasible generalized double k-class estimators under LINEX loss function is derived in a linear regression model. The disturbances are assumed to be non-spherical and their variance covariance matrix is unknown.