Estimation of more than one parameters in stratified sampling with fixed budget

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.     

An optimum multivariate stratified double sampling design in presence of non-response

In stratified sampling when strata weights are unknown double sampling technique may be used to estimate them. At first a large simple random sample from the population without considering the stratification is drawn and sampled units belonging to each stratum are recorded to estimate the unknown strata weights. A stratified random sample is then obtained comprising of simple random subsamples out of the previously selected units of the strata. If the problem of non-response is there, then these subsamples may be divided into classes of respondents and non-respondents. A second subsample is then drawn out of non-respondents and an attempt is made to obtain the information. This procedure is called Double Sampling for Stratification (DSS). Okafor (Aligarh J Statist 14:13–23, 1994) derived DSS estimators based on the subsampling of non-respondents. Najmussehar and Bari (Aligarh J Statist 22:27–41, 2002) discussed an optimum double sampling design by formulating the problem as a mathematical programming problem and used the dynamic programming technique to solve it. In the present paper a multivariate stratified population is considered with unknown strata weights and an optimum sampling design is proposed in the presence of non-response to estimate the unknown population means using DSS strategy. The problem turns out to be a multiobjective integer nonlinear programming problem. A solution procedure is developed using Goal Programming technique. A numerical example is presented to illustrate the computational details.