Optimum allocation in stratified random sampling via Holder's inequality
Attila Csenki · Journal of the Royal Statistical Society Series D (The Statistician) · 1997
Optimum allocation in stratified random sampling leads to a constrained optimization problem which is usually solved by any of the following three approaches: by Lagrange multipliers, by converting the problem into an unconstrained optimization problem or, if the cost is a linear funct ion of the stratum sample sizes, by an argument involving the Cauchy–Schwarz inequality. The last of these three methods is extended here by way of Hölder’s inequality to cover the case when the cost is a linear combination of some power of the stratum sample sizes. This approach has several advantages: it is elementary, it covers a broad class of cost functions and it avoids the back-substitu tion argument which, though elementary, tends to be cumbersome