zbMATH — the first resource for mathematics

Linear statistical models with constraints revisited. (English) Zbl 0851.62050
Summary: In the practice, two classes of basic linear models with constraints occur, i.e., models with observations of a complete first order vector parameter and models with observations of an incomplete first order vector parameter. In the former class, the locally best linear unbiased estimators are known explicitly. In the latter class, they are given by algorithms.
Explicit formulae for these estimators are given and the effects of constraints on the estimators in the form of suitable projection operators correcting estimators non respecting these constraints are investigated in both of the classes.

62J05 Linear regression; mixed models
62F30 Parametric inference under constraints
62H12 Estimation in multivariate analysis
62F10 Point estimation
Full Text: EuDML
[1] KUBÁČEK L.: Foundations of Estimation Theory. Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988. · Zbl 0698.62004
[2] KUBÁČEK L.: Equivalent algorithms for estimation in linear model with condition. Math. Slovaca 41 (1991), 401-421. · Zbl 0762.62018
[3] KUBÁČKOVÁ L.: Foundations of Experimental Data Analysis. CRC Press, Boca Raton-Ann Arbor-London-Tokyo, 1992. · Zbl 0875.62016
[4] RAO C. R.: Unified theory of linear estimation. Sankhyā Ser. A 33 (1971), 370-396. · Zbl 0236.62048
[5] RAO C. R., MITRA S. K.: Generalized Inverse of Matrices and Its Applications. J. Wiley, New York, 1971. · Zbl 0236.15005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.