Mean Estimation in Adaptive Cluster Sampling using Auxiliary Information

Abstract

In this dissertation, generalized simple and exponential type estimators have been developed using the information of single and two auxiliary variables for the estimation of rare and clustered population mean in adaptive cluster sampling designs. The proposed estimators are specifically developed for different situations of clustered populations in simple adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling designs.

In Chapter 1, the discussion has been made about the situations of rare and clustered population in which the conventional sampling designs may not be appropriate in order to achieve even moderate precision. The use of adaptive cluster sampling design along with the process in the presence of auxiliary information is also discussed. Comparison of adaptive cluster sampling with conventional sampling design and some advantages and disadvantages has also been given. Furthermore, stratified adaptive cluster sampling and systematic adaptive cluster sampling has been illustrated in the same Chapter with the detail sampling process. In Chapter 2, the literature regarding the use of auxiliary information in conventional sampling designs, adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling have been discussed whereas Chapter 3 contains some basic estimators that already developed in conventional sampling designs, adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling designs.

The major contribution of this dissertation appears from Chapter 4 by proposing modified ratio and regression-cum-modified ratio estimators using the information of single auxiliary variable in adaptive cluster sampling by utilizing the average values of the networks with simple random sampling without replacement. The expressions of approximate bias and mean square error for the proposed estimators have been derived. The generalized form for the proposed estimators has been suggested by introduction the unknown constants. The expressions of approximate bias and mean square error have been derived for the generalized form and optimum properties have been discussed. Many conventional and non-conventional parameters of the auxiliary variable have been used as special cases of the proposed estimators. The efficiency issues in adaptive cluster sampling have also been discussed. Theoretical comparisons have been made of the proposed estimators with existing estimators. An extensive numerical study is conducted by using real and artificial population data sets for all the estimators to evaluate their performance.

In Chapter 5, weighted exponential ratio-product type estimator have been developed using single auxiliary variable in adaptive cluster sampling for the situations in which the relationship between the survey variable and the auxiliary variable is non-linear. The expressions of approximate bias and mean square error have been derived. A simulation study is conducted to evaluate the performance of the proposed estimator with existing exponential type estimators.

In Chapter 6, a generalized semi-exponential type estimator has been suggested based on two auxiliary variables in adaptive cluster sampling. Some exponential and non-exponential type estimators have been discussed, as the special cases of the proposed estimator. The expressions of estimated bias and minimum mean square error have been derived. A simulation study is conducted on simulated populations generated by Poisson cluster process and Ecodist Package in R, to examining the performance of proposed estimator in adaptive cluster sampling design.

In Chapter 7, modified ratio and regression-cum-modified ratio estimators have been developed using the information of single auxiliary variable in stratified adaptive cluster sampling. The generalized form for the proposed estimators has been suggested by introduction the unknown constants. The expressions of approximate bias and mean square error have been derived and optimum properties have been discussed. Theoretical comparisons have been made of the proposed estimators with existing estimators. An extensive numerical study is conducted by using real and artificial population data sets for all the estimators to evaluate their performance.

In Chapter 8, a generalized semi-exponential type estimator has been suggested based on two auxiliary variables by utilizing the average values of the networks in stratified adaptive cluster sampling. Some exponential and nonexponential type estimators have been discussed, as the special cases of the proposed estimator. The expressions of approximate bias and minimum mean square error have also been derived. A simulation study is conducted using the simulated populations generated by Poisson cluster process at different level of rarity and aggregation to examining the performance of proposed estimator in stratified adaptive cluster sampling design.

In Chapter 9, modified ratio and regression-cum-modified ratio estimators have been developed using the information of single auxiliary variable in systematic adaptive cluster sampling. The generalized form for the proposed estimators has been suggested by introducing the unknown constants. The expressions of approximate bias and mean square error have been derived and optimum properties have been discussed. Theoretical comparison has been made of the proposed estimators with existing estimators. A numerical study is conducted by using artificial population data sets taken from Thompson (2012) for all the estimators to evaluate their performance.