Normal approximations to sums of scores based on occupancy numbers
Let \((U_ 1,...,U_ n)\) be a multinomial random vector with parameters \((N;p_ 1,...,p_ n)\) and let \(\{\) C(j,k),\(j\geq 0,k=1,2,...,n\}\) be a set of constants, depending upon N. Define \(S=\sum^{n}_{k=1}C(U_ k,k)\), which is known as the sum of scores based on occupancy numbers. In this paper, the authors proved the asymptotic normality of S as N, \(n\to \infty\), under certain conditions. \textit{C. Morris} [Ann. Stat. 3, 165-188 (1975; Zbl 0305.62013)] established the same result under conditions which neither imply nor are implied by those conditions imposed in this paper. Also, the authors mainly establish the bounds of the rates of this convergence under various conditions.
scientific article; zbMATH DE number 3936090