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Local large deviation theorem for sums of i.i.d. random vectors when the Cramér condition holds in the whole space

Juszczak D., Nagaev A. V.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

297--320

A class of multidimensional distributions is considered. This class contains all the elliptically contoured distributions having sup-exponential weight function. Each representative of the class determines a family of the so-called exponential or conjugate distributions. It is established that the conjugate distribution is asymptotically normal. On the basis of this normality a large deviation local limit theorem is proved. The theorem assumes no restrictions on the order of deviations.