Stein rule prediction of the composite target function in a general linear regression model. (English) Zbl 0953.62064
Summary: 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 the 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.
Keywords:
BLUP; MSE matrix; quadratic loss; target function; mean squared error; Stein rule predictors; best linear unbiased predictorReferences:
| [1] | Chaturvedi, A.; Shukla, G., Stein Rule Estimation in Linear Model with Nonscalar Error Covariance Matrix, Sankhyā B, 52, 293-304 (1990) · Zbl 0746.62057 |
| [2] | Copas, J. B., Regression, prediction and Shrinkage (with discussion), Journal of Royal Statistical Society, B, 45, 311-354 (1983) · Zbl 0532.62048 |
| [3] | Copas, J. B.; Jones, M. C., Regression Shrinkage Methods and Autoregressive Time Series Prediction, Australian Journal of Statistics, 29, 264-277 (1987) · doi:10.1111/j.1467-842X.1987.tb00744.x |
| [4] | Gotway, C. A.; Cressie, N., Improved Multivariate Prediction under a General Linear Model, Journal of Multivariate Analysis, 45, 56-72 (1993) · Zbl 0767.62060 · doi:10.1006/jmva.1993.1026 |
| [5] | Judge, G. G.; Bock, M. E., The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics (1978), New York: John Wiley and Sons, New York · Zbl 0395.62078 |
| [6] | Judge, G. G.; Griffiths, W. E.; Hill, R. C.; Lütkepohl, H.; Lee, T. C., The Theory and Practice of Econometrics (1985), New York: John Wiley and Sons, New York |
| [7] | 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. |
| [8] | Shalabh, Unbiased Prediction in Linear Regression Models with Equi-Correlated Responses, Statistical Papers, 39, 237-244 (1998) · Zbl 0887.62076 · doi:10.1007/BF02925411 |
| [9] | Srivastava, A. K.; Shalabh, A Composite Target Function for Prediction in Econometric Models, Indian Journal of Applied Econometrics, 5, 251-257 (1996) |
| [10] | Theil, H., Principle of Econometrics (1971), New York: John Wiley and Sons, New York |
| [11] | Toutenburg, H. Shalabh, Predictive Performance of the Methods of Restricted and Mixed Regression Estimators, Biometrical Journal, 38, 8, 951-959 (1996) · Zbl 0884.62075 · doi:10.1002/bimj.4710380807 |
| [12] | Vinod, H. D., Improved Stein Rule Estimator for Regression Problems, Journal of Econometrics, 12, 143-150 (1980) · Zbl 0431.62040 · doi:10.1016/0304-4076(80)90002-0 |
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