Variance Estimation in Coventional and Adaptive Cluster Sampling Designs

Abstract

In this dissertation, generalized simple and exponential type of estimators have been introduced to estimate limited population variance, utilizing the data from one auxiliary variables, under the framework of various sampling designs like as arbitrary random sampling, systematic sampling and adaptive cluster sampling design.

In Chapter 1, the discussion has been made about the designs of conventional sampling, the use of auxiliary information, single phase sampling procedures and adaptive cluster sampling procedures are given. Adaptive cluster sampling is suitable for the circumstances of rare and hidden populations in which conventional sampling design could not be suitable in order to attain the moderate precision. Some advantages and disadvantages has also been given.

In Chapter 2 the literature regarding conventional sampling designs and adaptive cluster sampling designs in simple and systematic sampling have been discussed. The main contribution of this dissertation has been appeared in Chapter 3, 4, 5, 6 and 7.

In Chapter 3 a class of generalized estimators based transformed auxiliary variables for population variance are suggested in simple random sampling without replacement using the mixture information of mean and variance as auxiliary information. Some further special cases have also been discussed for the suggested estimator. The generalized form for the suggested estimator has been suggested by introduction the unknown constants and also with the help of the coefficient of correlation, the coefficient of variation, the coefficient of skewness, the coefficient of kurtosis. The empirical results have been obtained for SRSWOR. The simulation results have also been showed for examining the performance of suggested estimators.

In Chapter 4 a generalized regression-cum-exponential estimators with two auxiliary variables for population variance have been developed under simple random sampling. Many exceptional cases of suggested estimators are obtained by using the different combinations of real numbers and some conventional parameters of assisting variable. The empirical and simulation study has also been exposed for examining the presentation of suggested estimators in arbitrary sampling.

In Chapter 5, modified regression-cum modified ratio estimators in variance estimators have been developed under the frame work of systematic sampling with single auxiliary variable. The generalized form of proposed x estimator has been discussed by introducing the unknown constants. Some special cases with the help of the coefficient of correlation, the coefficient of variation, the coefficient of skewness, and the coefficient of kurtosis, median, tri-mean and quartile deviation have been discussed by utilizing the systematic sampling technique for the estimation of finite population variance. The estimated bias and mean square error expression have been derived, up to first order of approximation. The Empirical and simulation study has also been conducted for examining the execution of proposed estimators in systematic sampling design.

In Chapter 6, a generalized estimator using single auxiliary variable in adaptive cluster sampling is proposed for the estimation of highly clumped rare and bunched population variance. We consider both situations in which the auxiliary variable is either positively or negatively connected with survey variable at unit just as the level of network. The proposed generalized estimator can produce a family of generalized estimators by using different combination of constants. The family of generalized estimators may produce many subfamilies of modified ratio and product-sort estimators utilizing distinctive combinations of real numbers and know traditional and non-conventional parameters of the auxiliary variable in place of α and γ. The mean square error and bias expressions have been inferred, up to first order of approximation. The simulation study has also been conducted in for examining the performance of proposed estimators in adaptive cluster sampling design.

In Chapter 7, joint influence of exponential ratio and exponential product type estimator have been made based on single auxiliary variable for the estimation of clustered population variance in adaptive cluster sampling design. When the correlation between study and auxiliary variable is non-linear then proposed estimator is suitable. The mean square error and bias expressions have been inferred, up to first order of approximation. The simulation study has also been conducted in examining the performance of proposed estimator in ACS design.