Exact maximum likelihood estimator of the structure of a stratified population

Abstract

An exact expression for the extreme values of the integer vector$\overline N = (N_1 , \ldots ,N_k )$ that maximize the function

$$\prod\limits_{j = 1}^k {\left( {\begin{array}{*{20}c} {N_j } \\ {l_j } \\ \end{array} } \right)} $$

for arbitrary integersl ₁>0, ...,l _k >0,k≥2, and a givenN ⁰=N ₁+...+N _k is derived. Also, statistical applications of the result are discussed.