Probabilities of large deviations in the case of stable limit distributions

Rate of convergence in the maximum likelihood estimation for partial discrete parameter, with applications to the cluster analysis and philology

“…ξ obeys a standard symmetric stable distribution with such a value of the parameter α. We derive analogously using the particular case of the results of Amosova [11] Q n ∼ C(α) n 1/α−1 , n → ∞. Let us assume again f 1 (x) = Ce −|x| f 0 (x).…”

“…and consider again the following estimation problem Θ = {0, 1}, Θ 1 = {1}, to put it differently, testing of statistical hypotheses. It follows from the main result of articles [11], [23], [37], [38], [42] that…”

Large deviations of sums of independent random variables from the domain of attraction of a stable law

“…The present paper deals with the case where the constant Cl in (1) is equal to zero but condition (4) fails (see [10,4,11]). In a certain sense, it is a continuation of the author's paper [6], where the case a = 2 was examined.…”

“…As in [6, (72 The necessity of condition (D~) with ~ = 1 is proved with the help of (54), (10), and (18) as was done in [6]. Condition (D~) mad relation (11) for ~ = 1 imply that for any ~ less than r and all n greater than n~, we have which holds for all 3' less than w2(5), some positive e = e(3'), and all sufficiently large n.…”