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A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models

Barbora Arendacká (2007)

Kybernetika

We consider a construction of approximate confidence intervals on the variance component σ 1 2 in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large σ 1 2 / σ 2 , was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when σ 1 2 / σ 2 suggests a modification of this interval that preserves some nice properties of the original and that...

A note on almost sure convergence and convergence in measure

P. Kříž, Josef Štěpán (2014)

Commentationes Mathematicae Universitatis Carolinae

The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.

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