The rate of convergence to the normal law for sampling without replacement. (Russian) Zbl 0574.60028

Mirakhmedov, Sh. A.

Teor. Veroyatn. Primen. 30, No. 3, 427-439 (1985).

Let \((\nu_{\ell 1},...,\nu_{\ell m})\) be a random Boolean vector, where \(\nu_{\ell m}=1\) if the m-th element of a finite population of volume N is chosen in the l-th sampling of volume \(n_{\ell}\) \((\ell =1,...,s)\), and \(\nu_{\ell m}=0\) otherwise, \(m=1,...,N\), \(\nu_{\ell 1}+...+\nu_{\ell N}=n_{\ell}\), \(\ell =1,...,s\). Let \(f_{jm}^{(N)}(x_ 1,...,x_ s)\) be a random function of a Boolean vector \((x_ 1,...,x_ s)\), \(j=1,...,k\); \(m=1,...,N\), and \(S_{jN}=\sum^{N}_{m=1}f_{jm}^{(N)}(\nu_{1m},..,\nu_{sm})\), \(j=1,...,k\). The rate of convergence of order 1/\(\sqrt{N}\) to a multidimensional normal law is proved for a vector \((S_{1N},...,S_{kN})\).

Reviewer: N.Leonenko

MSC:

60F05	Central limit and other weak theorems
60C05	Combinatorial probability

Keywords:

remainder term estimate; finite population; rate of convergence; multidimensional normal law