Kozachenko, Yu. V.; Moklyachuk, O. M. 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. Cited in 2 ReviewsCited in 2 Documents MSC: 60E15 Inequalities; stochastic orderings 60F10 Large deviations 62G05 Nonparametric estimation 62H10 Multivariate distribution of statistics Keywords:confidence regions; pre-Gaussian; square-Gaussian random vectors; probability of large deviations; stationary Gaussian processes PDFBibTeX XMLCite \textit{Yu. V. Kozachenko} and \textit{O. M. Moklyachuk}, Theory Probab. Math. Stat. 50, 1 (1994; Zbl 0861.60027); translation from Teor. Jmovirn. Mat. Stat. 50, 87--96 (1994)