Abstract
In this chapter, some basic definitions and results from matrix algebra, analysis, and probability theory are provided. These results were used throughout the previous chapters. It is our aim to provide unique notations when referring to elementary results and using some well-known mathematical techniques. Regarding more detailed explanations and derivations, we refer to the literature listed in the subsequent sections.
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References
Atiqullah M (1962) The estimation of residual variance in quadratically balanced least-squares problems and the robustness of the F-test. Biometrika 49:83–91
Basilevsky A (1983) Applied matrix algebra in the statistical sciences. North-Holland, Amsterdam
Dehling H, Haupt B (2004) Einführung in Die Wahrscheinlichkeitstheorie und Statistik, 2. Auflage. Springer, Heidelberg
Klenke A (2008) Wahrscheinlichkeitstheorie, 2. korrigierte Auflage. Springer, Heidelberg
Mathai AM, Provost SB (1992) Quadratic forms in random variables. Marcel Dekker, New York
Ogasawara T, Takahashi M (1951) Independence of quadratic forms in normal system. J Sci Hiroshima Univ 15:1–9
Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York
Rao CR, Rao MB (1998) Matrix algebra and its applications to statistics and econometrics. World Scientific, Singapore
Ravishanker N, Dey DK (2002) A first course in linear model theory. Chapman & Hall/CRC Press, Boca Raton
Schlittgen R (1996) Statistische Inferenz. Oldenbourg, München, Wien
Schott JR (2005) Matrix analysis for statistics. Chapman & Hall/CRC Press, Boca Raton
Van der Vaart, AW (1998) Asymptotic statistics. Cambridge University Press, Cambridge
Van der Vaart, AW (2000) Asymptotic statistics. Paperback edition. Cambridge University Press, Cambridge
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Brunner, E., Bathke, A.C., Konietschke, F. (2018). Mathematical Techniques. In: Rank and Pseudo-Rank Procedures for Independent Observations in Factorial Designs . Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-02914-2_8
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DOI: https://doi.org/10.1007/978-3-030-02914-2_8
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