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Keywords:
linear regression model; mean integrated square error; the best linear unbiased estimator and predictor; robustness; covariance matrix
linear regression model; mean integrated square error; the best linear unbiased estimator and predictor; robustness; covariance matrix
Summary:
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.
References:
[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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