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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) 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 provides invalid results in the presence of measurement errors in the data in the sense that sample R becomes an inconsistent estimator of(More)
  • Shalabh
  • J. Multivariate Analysis
  • 2013
This paper deals with the improved forecasts for the values of the study variable in linear regression models utilizing the minimum risk approach. It considers the simultaneous forecasting of actual and average values of the study variable and reports the performance properties of the classical unbiased forecasts and two biased forecasts with respect to the(More)
The restricted measurement error model is employed when certain study variables are not observable by direct measurement and if some information about the unknown regression coefficients is available a priori. In this study, we present a method for checking the goodness of fit in the restricted measurement error model. We obtain the goodness-offit(More)
This paper presents a general loss function under quadratic loss structure and discusses the comparison of risk functions associated with the unbiased least squares and biased Stein-rule estimators of the coefficients in a linear regression model. ∗Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India. E-mail:(More)
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