On asymptotic normality of randomized separable statistics in a generalized allocation scheme. (Russian) Zbl 0662.62012

Ivchenko, G. I.; Mirakhmedov, Sh. A.

Teor. Veroyatn. Primen. 33, No. 4, 807-813 (1988).

Let the joint distribution of \(\eta_ 1,\eta_ 2,...,\eta_ N\) coincide with the conditional distribution of non-negative integer-valued random variables \(\xi_ 1,\xi_ 2,...,\xi_ N\) given that \(\xi_ 1+\xi_ 2+...+\xi_ N=n\). The asymptotic properties of certain functionals of \(\eta_ 1,\eta_ 2,...,\eta_ N\) compose the essence of the so-called general occupancy problem. One of such functionals \(L_{Nn}=\sum^{N}_{m=1}f_{mN}(\eta_ m)\) known as a randomized divisible statistic is considered. Here \(f_{1N}(x_ 1),f_{2N}(x_ 2),...,f_{NN}(x_ N)\) is a triangular array of independent variables for every integer \(x_ 1,x_ 2,...,x_ N\). The asymptotic normality of \(L_{Nn}\) is established. The accuracy of normal approximation is also investigated.

Reviewer: A.V.Nagaev

MSC:

62E20	Asymptotic distribution theory in statistics
60F05	Central limit and other weak theorems

Keywords:

general occupancy problem; randomized divisible statistic; asymptotic normality; accuracy of normal approximation