Improved multivariate prediction in a general linear model with an unknown error covariance matrix

This paper deals with the problem of Stein-rule prediction in a general linear model. Our study extends the work of Gotway and Cressie (1993) by assuming that the covariance matrix of the model's disturbances is unknown. Also, predictions are based on a composite target function that incorporates allowance for the simultaneous predictions of the actual and average values of the target variable. We employ large sample asymptotic theory and derive and compare expressions for the bias vectors, mean squared error matrices, and risks based on a quadratic loss structure of the Stein-rule and the feasible best linear unbiased predictors. The results are applied to a model with first order autoregressive disturbances. Moreover, a Monte-Carlo experiment is conducted to explore the performance of the predictors in finite samples.

[1]  M. Schervish,et al.  Prior information in linear models , 1983 .

[2]  M. C. Jones,et al.  Regression Shrinkage Methods and Autoregressive Time Series Prediction , 1987 .

[3]  A. Chaturvedi,et al.  STEIN RULE ESTIMATION IN LINEAR MODEL WITH NONSCALAR ERROR COVARIANCE MATRIX , 1990 .

[4]  Alan T. K. Wan,et al.  Operational Variants of the Minimum Mean Squared Error Estimator in Linear Regression Models with Non-Spherical Disturbances , 2000 .

[5]  Y. Usami,et al.  Errata of Kariya and Toyooka (1992), “Bounds for normal approximations to the distributions of generalized least squares predictors and estimators” , 1997 .

[6]  Dale Borowiak,et al.  Linear Models, Least Squares and Alternatives , 2001, Technometrics.

[7]  J. Copas.  Regression, Prediction and Shrinkage , 1983 .

[8]  R. W. Farebrother,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[9]  Helge Toutenburg,et al.  Improved Predictions in Linear Regression Models with Stochastic Linear Constraints , 2000 .

[10]  Takeaki Kariya,et al.  Bounds for normal approximations to the distributions of generalized least squares predictors and estimators , 1992 .

[11]  Helge Toutenburg,et al.  Predictive Performance of the Methods of Restricted and Mixed Regression Estimators , 1996 .

[12]  Noel A Cressie,et al.  Improved multivariate prediction under a general linear model , 1993 .

[13]  Rand R. Wilcox,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[14]  Alan T. K. Wan,et al.  Double k -class estimators in regression models with non-spherical disturbances , 2001 .

[15]  Helge Toutenburg,et al.  Linear models : least squares and alternatives , 1999 .