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Statistische Methoden der Modellbildung. III: Statistische Inferenz für Kovarianzparameter. (German) Zbl 0556.62051
Mathematische Lehrbücher und Monographien. II. Abteilung: Mathematische Monographien, Bd. 45. Berlin: Akademie-Verlag. 344 S. M. 88.00 (1984).
[For Vol. II and I, see Zbl 0523.62064 and 353.62001, respectively.]
This book is the third volume on statistical inference methods written by the Mathematical-Statistics Collective at Humboldt University in Berlin and the Academy of Sciences of the DDR. It is an effort to summarize the current status of inference in covariance-structure models. The book is split into three chapters, dealing with estimation of parameters in models with linear covariance structure, testing the structure of covariance matrices and testing in variance-component models, respectively. The presentation is fairly rigorous, with proofs of various optimality properties.
Reviewer: J.Lillestøl

62J10 Analysis of variance and covariance (ANOVA)
62H12 Estimation in multivariate analysis
62H15 Hypothesis testing in multivariate analysis
62-02 Research exposition (monographs, survey articles) pertaining to statistics