an:04082619
Zbl 0662.60041
Sirazhdinov, S. Kh.; Mirakhmedov, Sh. A.; Ismatullaev, Sh. A.
Deviation probabilities for randomized decomposable statistics in a polynomial scheme
EN
Sov. Math., Dokl. 36, 583-585 (1988); translation from Dokl. Akad. Nauk SSSR 297, 1062-1064 (1987).
00180181
1988
j
60F10 62E20
polynomial scheme; randomized decomposable statistic; large deviation asymptotics
Consider a randomized decomposable statistic, i.e. \(R_ N=\sum^{N}_{1}f_{mN}(\nu_ m)\), where \(\nu =(\nu_ 1,...,\nu_ N)\) has a polynomial distribution \(M(n;p_ 1,...,p_ n)\) and \(f_{mN}(x)\) is a random function of the nonnegative integer argument x, \(m=1,...,N.\)
The authors present four theorems (without proofs) establishing large deviation asymptotics of \(P(R_ N>x(Var R_ N)^{1/2})\) in the zones \(x=O((\log N)^{1/2})\), \(x=o(N^{1/6})\), \(x=o(N^{1/2})\), and \(x\sim const N^{1/2}\), under the corresponding conditions on the functions \(f_{mN}(\cdot)\).
J.Steinebach