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Pre-Gaussian random vectors and their applications. (English. Ukrainian original) Zbl 0861.60027

Theory Probab. Math. Stat. 50, 89-98 (1995); translation from Teor. Jmovirn. Mat. Stat. 50, 87-96 (1994).
Summary: Definitions of pre-Gaussian and square-Gaussian random vectors are given. Properties of these vectors are investigated. Estimates are derived for the probability of large deviations of sums of independent random vectors with the help of the properties obtained. Confidence regions are constructed for covariance functions and mathematical expectations of stationary Gaussian processes.

MSC:

60E15 Inequalities; stochastic orderings
60F10 Large deviations
62G05 Nonparametric estimation
62H10 Multivariate distribution of statistics
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