Optimum stratification using auxiliary variables

The problem of determining optimum strata boundaries (OSB), when the frequency distribution of survey (or main) information is known, is discussed by many authors and is available in sampling literature. However, many of these authors made an unrealistic assumption that the frequency distribution of study variable is known prior to conducting the survey. In this manuscript, we discuss the problems of determining the optimum stratifications, when the frequency distribution of auxiliary variable is known. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. Moreover, often the auxiliary information is easily available or can be made available with a minimum cost and effort. In this manuscript, the problems of constructing optimum stratification is discussed for two study variables based on the auxiliary variables that follow respectively a uniform and a right-triangular distribution. The problems of determining the OSB are formulated as Nonlinear Programming Problems (NLPP), which turn out to be multistage decision problems and are solved using dynamic programming techniques