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Article

Stability of characterization of the independence of random variables by the independence of linear statistics.

Theory of Probability and Its Applications. 2015. Vol. 59. No. 4. P. 179-190.
Belomestny D., Prokhorov A.

Let  (X1; Y1),..., (XN; YN) be independent identically distributed random vectors. We show, that if the statistics LX = a1*X1+...  + aN*XN and LY = b 1*Y1 + ...  + b N*YN are epsilon - independent, then under some conditions X = (X1,..., XN),  Y = (Y1,..., YN) are "epsilon in the power alpha"-independent for some alpha> 0.