By Pierre Lelong

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**Extra resources for Seminaire Pierre Lelong (Analyse) Annee 1975-76**

**Example text**

N . 7) we find that Jacobian is equal to J(Yn,UJ = det[ I" OIl>

4) 1=1 J=1 then Jex - y2 /2dy (21t)1/2 .

Generalized variance is an important measure of spread in multidimensional statistical analysis. In this chapter we develop a general analysis for it, when observed random vectors Xl, ... ,X" do not have density and its components have an arbitrary dependence structure. It is natural that in this case we must use asymptotic methods, when dimension of observed vectors mayaiso increase together with the growing number of observations. Under certain conditions the central limit theorem for empirical generalized variance is proven.