Titlebook: Applied Multivariate Statistical Analysis; Wolfgang H?rdle,Léopold Simar Textbook 20072nd edition Springer-Verlag Berlin Heidelberg 2007 A

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Multivariate Distributionsation on the relationship between the variables can be made available. Only basic statistical theory was used to derive tests of independence or of linear relationships. In this chapter we give an introduction to the basic probability tools useful in statistical multivariate analysis.

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Theory of the Multinormalistribution, 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 a

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Theory of Estimation generates the data. This is known as statistical inference: we infer from information contained in a sample properties of the population from which the observations are taken. In multivariate statistical inference, we do exactly the same. The basic ideas were introduced in Section 4.5 on sampling t

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Decomposition of Data Matrices by Factorsvariate or univariate devices used to reduce the dimensions of the observations. In the following three chapters, issues of reducing the dimension of a multivariate data set will be discussed. The perspectives will be different but the tools will be related.

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Cluster Analysissituations can arise. Given a data set containing measurements on individuals, in some cases we want to see if some natural groups or classes of individuals exist, and in other cases, we want to classify the individuals according to a set of existing groups. Cluster analysis develops tools and metho

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Multidimensional Scalingt Analysis are dominantly used tools. In many applied sciences data is recorded as ranked information. For example, in marketing, one may record “product A is better than product B”. High-dimensional observations therefore often have mixed data characteristics and contain relative information (w.r.t