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Classical regression model under zero-excess assumptions. (English) Zbl 0847.62053

Summary: We consider the classical regression model defined by a random vector \(X_{n \times 1}\), scalar matrices \(y_{n \times m}\), \(v_{n \times n}\), a scalar column \(b_{m \times 1}\) and a scalar \(s^2\) satisfying \(EX = yb\), \(\text{Cov } X = s^2 v\) and the usual regularity conditions. Using only zero-excess assumptions, we prove that the classical estimator \(\widehat{s}^2\) for \(s^2\) in that model is the unique unbiased one with minimum variance in a large class of estimators.

MSC:

62J05 Linear regression; mixed models
62J99 Linear inference, regression
62H12 Estimation in multivariate analysis
46N30 Applications of functional analysis in probability theory and statistics
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References:

[1] Cramér, H., Mathematical Methods in Statistics (1946), Princeton University Press: Princeton University Press Princeton
[2] F. De Vylder and M. Goovaerts, Optimal parameter estimation under zero excess assumptions in a classical model, (forthcoming).; F. De Vylder and M. Goovaerts, Optimal parameter estimation under zero excess assumptions in a classical model, (forthcoming). · Zbl 0752.62076
[3] F. De Vylder, and M. Goovaerts, Classical model with several random vectors under zero excess assumptions, (forthcoming).; F. De Vylder, and M. Goovaerts, Classical model with several random vectors under zero excess assumptions, (forthcoming). · Zbl 0847.62053
[4] Scheffé, H., The Analysis of Variance (1959), Wiley: Wiley New York · Zbl 0086.34603
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