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Multistage regression model

Lubomír Kubáček — 1986

Aplikace matematiky

Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) β ^ i ( Y 1 , , Y i ) is identical with the BLUE β ^ i ( β ^ 1 , , β ^ i - 1 , Y i ) ; Y 1 , Y i are subvectors of the random vector Y in a general regression model ( Y , X β , ) , ( β 1 ' , , β i ' ) ' = β a vector of unknown parameters; the design matrix X having a special so called multistage struture and the covariance matrix are given.

Multivariate models with constraints confidence regions

Lubomír Kubáček — 2008

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can...

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