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linear regression model; mean integrated square error; the best linear unbiased estimator and predictor; robustness; covariance matrix
If is shown that in linear regression models we do not make a great mistake if we substitute some sufficiently precise approximations for the unknown covariance matrix and covariance vector in the expressions for computation of the best linear unbiased estimator and predictor.
[1] E. Parzen: Time series analysis papers. Holden - Day, San Francisco 1967. MR 0223042 | Zbl 0171.39602
[2] C. R. Rao: Linear statistical inference and its applications. Wiley, New-York 1965. MR 0221616 | Zbl 0137.36203
[3] O. N. Strand: Coefficient errors caused by using the wrong covariance matrix in the general linear regression model. Ann. Stat. (2), 1974, 935-949. DOI 10.1214/aos/1176342815 | MR 0356378
[4] F. Štulajter: Estimators with minimal mean integrated square error in regression models. Submitted to Statistics.
[5] F. Štulajter: Estimation in random processes. SNTL - Alfa, Bratislava (to appear in 1989).
[6] B. Z. Vulich: An introduction to functional analysis. (Russian). Nauka, Moscow 1967. MR 0218864
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