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Deviation probabilities for randomized decomposable statistics in a polynomial scheme. (English. Russian original) Zbl 0662.60041
Sov. Math., Dokl. 36, 583-585 (1988); translation from Dokl. Akad. Nauk SSSR 297, 1062-1064 (1987).
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 $$f_{mN}(\cdot)$$.
Reviewer: J.Steinebach
##### MSC:
 60F10 Large deviations 62E20 Asymptotic distribution theory in statistics