| || || Prasad, Vikashni Devi|
| || || Non linear programming in stratified random sampling and two-stage sampling |
Author:Prasad, Vikashni Devi
Institution: University of the South Pacific.
Call No.: Pac QA 276 .6 .P73 2012
Copyright:Under 10% of this thesis may be copied without the authors written permission
Abstract: The problem of determining optimum stratum boundaries (OSB) when the frequency distribution of survey (or main) variable is known, is discussed by many authors and is available in sampling literature. However, many of these attempts have been made with an unrealistic assumption that the frequency distribution of the study variable y which is unavailable prior to conducting survey, is known. Often, the data on another variable x (known as the auxiliary variable) highly correlated with y are available. For example, the data on the size of land ( x ) cultivated which are highly correlated with the amount of crop ( y ), are easily available. It is, therefore, if the stratification is made based on the frequency distribution of x , it may lead to substantial gains in precision of the estimates, although it may not be as efficient as the one based on y . However, if the regression of y on x is high within all strata, the boundary points for both the variables should be nearly the same. In such a situation the OSB of the survey variable could be obtained using the frequency distribution of x , which can be estimated as the auxiliary data are readily available or can be made available easily. In chapter 2 and 3 in this manuscript, we discuss the problems of determining the optimum stratifications of two study variables based on the auxiliary variable that follows respectively a uniform and a right-triangular distribution in the population. These problems are formulated as Nonlinear Programming Problems (NLPP), which turn out to multistage decision problems and solved using dynamic programming techniques.