Abstract
In the preceding chapter we saw how the multivariate normal distribution comes into play in many applications. It is useful to know more about this distribution, since it is often a good approximate distribution in many situations. Another reason for considering the multinormal distribution relies on the fact that it has many appealing properties: it is stable under linear transforms, zero correlation corresponds to independence, the marginals and all the conditionals are also multivariate normal variates, etc. The mathematical properties of the multinormal make analyses much simpler.
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References
Fang, K. T., Kotz, S., & Ng, K. W. (1990). Symmetric multivariate and related distributions. London: Chapman and Hall.
Li, K.-C. (1992). On principal Hessian directions for data visualization and dimension reduction: Another application of Stein’s lemma. Journal of the American Statistical Association, 87, 1025–1039.
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Härdle, W.K., Simar, L. (2015). Theory of the Multinormal. In: Applied Multivariate Statistical Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45171-7_5
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DOI: https://doi.org/10.1007/978-3-662-45171-7_5
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