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Asymptotics of graphical projection pursuit. (English) Zbl 0559.62002
General conditions under which the asymptotic distribution of the almost all (with respect to the uniform measure on the unit ball of projecting vectors) projections is normal are given. Convergence in probability of empirical moments (of the first and second order) is also established. Arrays of random variables are proved to fulfil the mentioned general conditions and the upper bound of the distance between empirical distributions of projections and normal distributions is derived (this distance is a random variable with respect to the uniform measure on the unit ball).
Examples of nonnormal asymptotic distributions of projections are exposed, too. Many interesting issues, arising e.g. from relations of size of sample and dimension of data vectors, are discussed and generalizations for two-dimensional projections are sketched.
Reviewer: J.Á.Víšek

MSC:
62-07 Data analysis (statistics) (MSC2010)
62E20 Asymptotic distribution theory in statistics
60F99 Limit theorems in probability theory
62H10 Multivariate distribution of statistics
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