Abstract
This paper considers the problem of simultaneous prediction of the actual and average values of the dependent variable in a general linear regression model. Utilizing the philosophy of Stein rule procedure, a family of improved predictors for a linear function of the actual and expected value of the dependent variable for the forecast period has been proposed. An unbiased estimator for the mean squared error (MSE) matrix of the proposed family of predictors has been obtained and dominance of the family of Stein rule predictors over the best linear unbiased predictor (BLUP) has been established under a quadratic loss function.
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References
Chaturvedi, A. and Shukla, G. (1990): Stein Rule Estimation in Linear Model with Nonscalar Error Covariance Matrix, Sankhyā B, 52, 293–304.
Copas, J.B. (1983): Regression, prediction and Shrinkage (with discussion), Journal of Royal Statistical Society, B, 45, 311–354.
Copas, J.B. and Jones, M.C. (1987): Regression Shrinkage Methods and Autoregressive Time Series Prediction, Australian Journal of Statistics, 29, 264–277.
Gotway, C.A. and Cressie, N. (1993): Improved Multivariate Prediction under a General Linear Model, Journal of Multivariate Analysis, 45, 56–72.
Judge, G.G. and Bock, M.E. (1978): The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics, John Wiley and Sons, New York.
Judge, G.G., Griffiths, W.E. Hill, R.C. Lütkepohl, H. and Lee, T.C. (1985): The Theory and Practice of Econometrics, John Wiley and Sons, New York.
Shalabh (1995): Performance of Stein-Rule Procedure for Simultaneous Prediction of Actual and Average Values of Study Variable in Linear Regression Model, Bulletin of the International Statistical Institute, 1375–1390.
Shalabh (1998): Unbiased Prediction in Linear Regression Models with Equi-Correlated Responses, Statistical Papers, 39, 237–244.
Srivastava, A.K. and Shalabh (1996): A Composite Target Function for Prediction in Econometric Models, Indian Journal of Applied Econometrics, 5, 251–257.
Theil, H. (1971): Principle of Econometrics, John Wiley and Sons, New York.
Toutenburg, H. Shalabh (1996): Predictive Performance of the Methods of Restricted and Mixed Regression Estimators, Biometrical Journal, 38(8), 951–959.
Vinod, H.D. (1980): Improved Stein Rule Estimator for Regression Problems, Journal of Econometrics, 12, 143–150.
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Chaturvedi, A., Singh, S.P. Stein rule prediction of the composite target function in a general linear regression model. Statistical Papers 41, 359–367 (2000). https://doi.org/10.1007/BF02925929
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DOI: https://doi.org/10.1007/BF02925929