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Improved multivariate prediction in a general linear model with an unknown error covariance matrix. (English) Zbl 1043.62059
Summary: This paper deals with the problem of Stein-rule prediction in a general linear model. Our study extends the work of C. A. Gotway and N. Cressie [ibid. 45, 56–72 (1993; Zbl 0767.62060)] by assuming that the covariance matrix of the model 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.

MSC:
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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